Alles samen. Gebruik stappenplan en ZRM!
- \(-3(x-\frac{2}{7})=5x+\frac{10}{3}\)
- \(6(-5x+\frac{4}{13})=x+\frac{7}{16}\)
- \(7(-3x-\frac{3}{16})=-10x+\frac{2}{7}\)
- \(7(-x+\frac{4}{15})=6x+\frac{7}{16}\)
- \(2(-3x-\frac{4}{11})=7x+\frac{3}{10}\)
- \(3(-2x-\frac{3}{14})=5x+\frac{5}{4}\)
- \(-7(-2x-\frac{3}{5})=-9x+\frac{9}{4}\)
- \(-7(-5x+\frac{2}{5})=6x+\frac{9}{16}\)
- \(-(5x-\frac{2}{5})=2x+\frac{10}{11}\)
- \(-7(5x+\frac{4}{13})=4x+\frac{8}{3}\)
- \(-6(-4x+\frac{3}{2})=x+\frac{8}{3}\)
- \(-2(-4x+\frac{3}{14})=7x+\frac{7}{5}\)
Alles samen. Gebruik stappenplan en ZRM!
Verbetersleutel
- \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\
\begin{align}
& \color{red}{-3} (x-\frac{2}{7})& = & 5x+\frac{10}{3} \\\Leftrightarrow & -3x+\frac{6}{7}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(-3x+\frac{6}{7})& = & (5x+\frac{10}{3}). \color{blue}{21} \\\Leftrightarrow & -63x \color{red}{+18} & = & \color{red}{105x} +70 \\\Leftrightarrow & -63x \color{red}{+18} \color{blue}{-18} \color{blue}{-105x} & = & \color{red}{105x} +70 \color{blue}{-105x} \color{blue}{-18} \\\Leftrightarrow & -63x-105x& = & 70-18 \\\Leftrightarrow & \color{red}{-168} x& = & 52 \\\Leftrightarrow & x = \frac{52}{-168} & & \\\Leftrightarrow & x = \frac{-13}{42} & & \\ & V = \left\{ \frac{-13}{42} \right\} & \\\end{align}\)
- \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\
\begin{align}
& \color{red}{6} (-5x+\frac{4}{13})& = & x+\frac{7}{16} \\\Leftrightarrow & -30x+\frac{24}{13}& = & x+\frac{7}{16} \\ & & & \text{kgv van noemers 13 en 16 is 208} \\\Leftrightarrow & \color{blue}{208} .(-30x+\frac{24}{13})& = & (x+\frac{7}{16}). \color{blue}{208} \\\Leftrightarrow & -6240x \color{red}{+384} & = & \color{red}{208x} +91 \\\Leftrightarrow & -6240x \color{red}{+384} \color{blue}{-384} \color{blue}{-208x} & = & \color{red}{208x} +91 \color{blue}{-208x} \color{blue}{-384} \\\Leftrightarrow & -6240x-208x& = & 91-384 \\\Leftrightarrow & \color{red}{-6448} x& = & -293 \\\Leftrightarrow & x = \frac{-293}{-6448} & & \\\Leftrightarrow & x = \frac{293}{6448} & & \\ & V = \left\{ \frac{293}{6448} \right\} & \\\end{align}\)
- \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\
\begin{align}
& \color{red}{7} (-3x-\frac{3}{16})& = & -10x+\frac{2}{7} \\\Leftrightarrow & -21x-\frac{21}{16}& = & -10x+\frac{2}{7} \\ & & & \text{kgv van noemers 16 en 7 is 112} \\\Leftrightarrow & \color{blue}{112} .(-21x-\frac{21}{16})& = & (-10x+\frac{2}{7}). \color{blue}{112} \\\Leftrightarrow & -2352x \color{red}{-147} & = & \color{red}{-1120x} +32 \\\Leftrightarrow & -2352x \color{red}{-147} \color{blue}{+147} \color{blue}{+1120x} & = & \color{red}{-1120x} +32 \color{blue}{+1120x} \color{blue}{+147} \\\Leftrightarrow & -2352x+1120x& = & 32+147 \\\Leftrightarrow & \color{red}{-1232} x& = & 179 \\\Leftrightarrow & x = \frac{179}{-1232} & & \\\Leftrightarrow & x = \frac{-179}{1232} & & \\ & V = \left\{ \frac{-179}{1232} \right\} & \\\end{align}\)
- \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\
\begin{align}
& \color{red}{7} (-x+\frac{4}{15})& = & 6x+\frac{7}{16} \\\Leftrightarrow & -7x+\frac{28}{15}& = & 6x+\frac{7}{16} \\ & & & \text{kgv van noemers 15 en 16 is 240} \\\Leftrightarrow & \color{blue}{240} .(-7x+\frac{28}{15})& = & (6x+\frac{7}{16}). \color{blue}{240} \\\Leftrightarrow & -1680x \color{red}{+448} & = & \color{red}{1440x} +105 \\\Leftrightarrow & -1680x \color{red}{+448} \color{blue}{-448} \color{blue}{-1440x} & = & \color{red}{1440x} +105 \color{blue}{-1440x} \color{blue}{-448} \\\Leftrightarrow & -1680x-1440x& = & 105-448 \\\Leftrightarrow & \color{red}{-3120} x& = & -343 \\\Leftrightarrow & x = \frac{-343}{-3120} & & \\\Leftrightarrow & x = \frac{343}{3120} & & \\ & V = \left\{ \frac{343}{3120} \right\} & \\\end{align}\)
- \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\
\begin{align}
& \color{red}{2} (-3x-\frac{4}{11})& = & 7x+\frac{3}{10} \\\Leftrightarrow & -6x-\frac{8}{11}& = & 7x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(-6x-\frac{8}{11})& = & (7x+\frac{3}{10}). \color{blue}{110} \\\Leftrightarrow & -660x \color{red}{-80} & = & \color{red}{770x} +33 \\\Leftrightarrow & -660x \color{red}{-80} \color{blue}{+80} \color{blue}{-770x} & = & \color{red}{770x} +33 \color{blue}{-770x} \color{blue}{+80} \\\Leftrightarrow & -660x-770x& = & 33+80 \\\Leftrightarrow & \color{red}{-1430} x& = & 113 \\\Leftrightarrow & x = \frac{113}{-1430} & & \\\Leftrightarrow & x = \frac{-113}{1430} & & \\ & V = \left\{ \frac{-113}{1430} \right\} & \\\end{align}\)
- \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\
\begin{align}
& \color{red}{3} (-2x-\frac{3}{14})& = & 5x+\frac{5}{4} \\\Leftrightarrow & -6x-\frac{9}{14}& = & 5x+\frac{5}{4} \\ & & & \text{kgv van noemers 14 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(-6x-\frac{9}{14})& = & (5x+\frac{5}{4}). \color{blue}{28} \\\Leftrightarrow & -168x \color{red}{-18} & = & \color{red}{140x} +35 \\\Leftrightarrow & -168x \color{red}{-18} \color{blue}{+18} \color{blue}{-140x} & = & \color{red}{140x} +35 \color{blue}{-140x} \color{blue}{+18} \\\Leftrightarrow & -168x-140x& = & 35+18 \\\Leftrightarrow & \color{red}{-308} x& = & 53 \\\Leftrightarrow & x = \frac{53}{-308} & & \\\Leftrightarrow & x = \frac{-53}{308} & & \\ & V = \left\{ \frac{-53}{308} \right\} & \\\end{align}\)
- \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\
\begin{align}
& \color{red}{-7} (-2x-\frac{3}{5})& = & -9x+\frac{9}{4} \\\Leftrightarrow & 14x+\frac{21}{5}& = & -9x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(14x+\frac{21}{5})& = & (-9x+\frac{9}{4}). \color{blue}{20} \\\Leftrightarrow & 280x \color{red}{+84} & = & \color{red}{-180x} +45 \\\Leftrightarrow & 280x \color{red}{+84} \color{blue}{-84} \color{blue}{+180x} & = & \color{red}{-180x} +45 \color{blue}{+180x} \color{blue}{-84} \\\Leftrightarrow & 280x+180x& = & 45-84 \\\Leftrightarrow & \color{red}{460} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{460} & & \\ & V = \left\{ \frac{-39}{460} \right\} & \\\end{align}\)
- \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\
\begin{align}
& \color{red}{-7} (-5x+\frac{2}{5})& = & 6x+\frac{9}{16} \\\Leftrightarrow & 35x-\frac{14}{5}& = & 6x+\frac{9}{16} \\ & & & \text{kgv van noemers 5 en 16 is 80} \\\Leftrightarrow & \color{blue}{80} .(35x-\frac{14}{5})& = & (6x+\frac{9}{16}). \color{blue}{80} \\\Leftrightarrow & 2800x \color{red}{-224} & = & \color{red}{480x} +45 \\\Leftrightarrow & 2800x \color{red}{-224} \color{blue}{+224} \color{blue}{-480x} & = & \color{red}{480x} +45 \color{blue}{-480x} \color{blue}{+224} \\\Leftrightarrow & 2800x-480x& = & 45+224 \\\Leftrightarrow & \color{red}{2320} x& = & 269 \\\Leftrightarrow & x = \frac{269}{2320} & & \\ & V = \left\{ \frac{269}{2320} \right\} & \\\end{align}\)
- \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\
\begin{align}
& \color{red}{-} (5x-\frac{2}{5})& = & 2x+\frac{10}{11} \\\Leftrightarrow & -5x+\frac{2}{5}& = & 2x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(-5x+\frac{2}{5})& = & (2x+\frac{10}{11}). \color{blue}{55} \\\Leftrightarrow & -275x \color{red}{+22} & = & \color{red}{110x} +50 \\\Leftrightarrow & -275x \color{red}{+22} \color{blue}{-22} \color{blue}{-110x} & = & \color{red}{110x} +50 \color{blue}{-110x} \color{blue}{-22} \\\Leftrightarrow & -275x-110x& = & 50-22 \\\Leftrightarrow & \color{red}{-385} x& = & 28 \\\Leftrightarrow & x = \frac{28}{-385} & & \\\Leftrightarrow & x = \frac{-4}{55} & & \\ & V = \left\{ \frac{-4}{55} \right\} & \\\end{align}\)
- \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\
\begin{align}
& \color{red}{-7} (5x+\frac{4}{13})& = & 4x+\frac{8}{3} \\\Leftrightarrow & -35x-\frac{28}{13}& = & 4x+\frac{8}{3} \\ & & & \text{kgv van noemers 13 en 3 is 39} \\\Leftrightarrow & \color{blue}{39} .(-35x-\frac{28}{13})& = & (4x+\frac{8}{3}). \color{blue}{39} \\\Leftrightarrow & -1365x \color{red}{-84} & = & \color{red}{156x} +104 \\\Leftrightarrow & -1365x \color{red}{-84} \color{blue}{+84} \color{blue}{-156x} & = & \color{red}{156x} +104 \color{blue}{-156x} \color{blue}{+84} \\\Leftrightarrow & -1365x-156x& = & 104+84 \\\Leftrightarrow & \color{red}{-1521} x& = & 188 \\\Leftrightarrow & x = \frac{188}{-1521} & & \\\Leftrightarrow & x = \frac{-188}{1521} & & \\ & V = \left\{ \frac{-188}{1521} \right\} & \\\end{align}\)
- \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\
\begin{align}
& \color{red}{-6} (-4x+\frac{3}{2})& = & x+\frac{8}{3} \\\Leftrightarrow & 24x-9& = & x+\frac{8}{3} \\ & & & \text{kgv van noemers 1 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(24x-9)& = & (x+\frac{8}{3}). \color{blue}{3} \\\Leftrightarrow & 72x \color{red}{-27} & = & \color{red}{3x} +8 \\\Leftrightarrow & 72x \color{red}{-27} \color{blue}{+27} \color{blue}{-3x} & = & \color{red}{3x} +8 \color{blue}{-3x} \color{blue}{+27} \\\Leftrightarrow & 72x-3x& = & 8+27 \\\Leftrightarrow & \color{red}{69} x& = & 35 \\\Leftrightarrow & x = \frac{35}{69} & & \\ & V = \left\{ \frac{35}{69} \right\} & \\\end{align}\)
- \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\
\begin{align}
& \color{red}{-2} (-4x+\frac{3}{14})& = & 7x+\frac{7}{5} \\\Leftrightarrow & 8x-\frac{3}{7}& = & 7x+\frac{7}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(8x-\frac{3}{7})& = & (7x+\frac{7}{5}). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{-15} & = & \color{red}{245x} +49 \\\Leftrightarrow & 280x \color{red}{-15} \color{blue}{+15} \color{blue}{-245x} & = & \color{red}{245x} +49 \color{blue}{-245x} \color{blue}{+15} \\\Leftrightarrow & 280x-245x& = & 49+15 \\\Leftrightarrow & \color{red}{35} x& = & 64 \\\Leftrightarrow & x = \frac{64}{35} & & \\ & V = \left\{ \frac{64}{35} \right\} & \\\end{align}\)