Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(4(-4x-6)=-6-(-10+3x)\)
2. \(4(-x-7)=1+(-10+x)\)
3. \(3(-6x-5)=-12-(7+17x)\)
4. \(4(x+1)=15+(2+x)\)
5. \(2(2x+2)=1-(-5+3x)\)
6. \(3(5x+4)=-11-(14+x)\)
7. \(5(-3x-6)=6+(-9+4x)\)
8. \(2(-5x-5)=-3+(-1+x)\)
9. \(6(4x+7)=10-(-1+5x)\)
10. \(3(6x+4)=1-(-7+5x)\)
11. \(4(3x-7)=13-(-3+5x)\)
12. \(5(4x-7)=6-(-7+19x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-4x-6)& = & -6 \color{red}{-} (-10+3x) \\\Leftrightarrow & -16x-24& = &-6+10-3x \\\Leftrightarrow & -16x \color{red}{-24} & = &4 \color{red}{-3x} \\\Leftrightarrow & -16x \color{red}{-24} \color{blue}{+24} \color{blue}{+3x} & = &4 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+24} \\\Leftrightarrow & -16x+3x& = &4+24 \\\Leftrightarrow & -13x& = &28 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{28}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-28}{13} & & \\ & V = \left\{ \frac{-28}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-x-7)& = & 1 \color{red}{+} (-10+x) \\\Leftrightarrow & -4x-28& = &1-10+x \\\Leftrightarrow & -4x \color{red}{-28} & = &-9 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & -4x-x& = &-9+28 \\\Leftrightarrow & -5x& = &19 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{19}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-19}{5} & & \\ & V = \left\{ \frac{-19}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-6x-5)& = & -12 \color{red}{-} (7+17x) \\\Leftrightarrow & -18x-15& = &-12-7-17x \\\Leftrightarrow & -18x \color{red}{-15} & = &-19 \color{red}{-17x} \\\Leftrightarrow & -18x \color{red}{-15} \color{blue}{+15} \color{blue}{+17x} & = &-19 \color{red}{-17x} \color{blue}{+17x} \color{blue}{+15} \\\Leftrightarrow & -18x+17x& = &-19+15 \\\Leftrightarrow & -x& = &-4 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-4}{ \color{red}{-1} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (x+1)& = & 15 \color{red}{+} (2+x) \\\Leftrightarrow & 4x+4& = &15+2+x \\\Leftrightarrow & 4x \color{red}{+4} & = &17 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &17 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 4x-x& = &17-4 \\\Leftrightarrow & 3x& = &13 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{13}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{13}{3} & & \\ & V = \left\{ \frac{13}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (2x+2)& = & 1 \color{red}{-} (-5+3x) \\\Leftrightarrow & 4x+4& = &1+5-3x \\\Leftrightarrow & 4x \color{red}{+4} & = &6 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+4} \color{blue}{-4} \color{blue}{+3x} & = &6 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-4} \\\Leftrightarrow & 4x+3x& = &6-4 \\\Leftrightarrow & 7x& = &2 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{2}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{2}{7} & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (5x+4)& = & -11 \color{red}{-} (14+x) \\\Leftrightarrow & 15x+12& = &-11-14-x \\\Leftrightarrow & 15x \color{red}{+12} & = &-25 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-25 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 15x+x& = &-25-12 \\\Leftrightarrow & 16x& = &-37 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{-37}{ \color{red}{16} } \\\Leftrightarrow & x = \frac{-37}{16} & & \\ & V = \left\{ \frac{-37}{16} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-3x-6)& = & 6 \color{red}{+} (-9+4x) \\\Leftrightarrow & -15x-30& = &6-9+4x \\\Leftrightarrow & -15x \color{red}{-30} & = &-3 \color{red}{+4x} \\\Leftrightarrow & -15x \color{red}{-30} \color{blue}{+30} \color{blue}{-4x} & = &-3 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+30} \\\Leftrightarrow & -15x-4x& = &-3+30 \\\Leftrightarrow & -19x& = &27 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{27}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-27}{19} & & \\ & V = \left\{ \frac{-27}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-5x-5)& = & -3 \color{red}{+} (-1+x) \\\Leftrightarrow & -10x-10& = &-3-1+x \\\Leftrightarrow & -10x \color{red}{-10} & = &-4 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & -10x-x& = &-4+10 \\\Leftrightarrow & -11x& = &6 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{6}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-6}{11} & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (4x+7)& = & 10 \color{red}{-} (-1+5x) \\\Leftrightarrow & 24x+42& = &10+1-5x \\\Leftrightarrow & 24x \color{red}{+42} & = &11 \color{red}{-5x} \\\Leftrightarrow & 24x \color{red}{+42} \color{blue}{-42} \color{blue}{+5x} & = &11 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-42} \\\Leftrightarrow & 24x+5x& = &11-42 \\\Leftrightarrow & 29x& = &-31 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-31}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-31}{29} & & \\ & V = \left\{ \frac{-31}{29} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (6x+4)& = & 1 \color{red}{-} (-7+5x) \\\Leftrightarrow & 18x+12& = &1+7-5x \\\Leftrightarrow & 18x \color{red}{+12} & = &8 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{+12} \color{blue}{-12} \color{blue}{+5x} & = &8 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-12} \\\Leftrightarrow & 18x+5x& = &8-12 \\\Leftrightarrow & 23x& = &-4 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-4}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-4}{23} & & \\ & V = \left\{ \frac{-4}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (3x-7)& = & 13 \color{red}{-} (-3+5x) \\\Leftrightarrow & 12x-28& = &13+3-5x \\\Leftrightarrow & 12x \color{red}{-28} & = &16 \color{red}{-5x} \\\Leftrightarrow & 12x \color{red}{-28} \color{blue}{+28} \color{blue}{+5x} & = &16 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+28} \\\Leftrightarrow & 12x+5x& = &16+28 \\\Leftrightarrow & 17x& = &44 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{44}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{44}{17} & & \\ & V = \left\{ \frac{44}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (4x-7)& = & 6 \color{red}{-} (-7+19x) \\\Leftrightarrow & 20x-35& = &6+7-19x \\\Leftrightarrow & 20x \color{red}{-35} & = &13 \color{red}{-19x} \\\Leftrightarrow & 20x \color{red}{-35} \color{blue}{+35} \color{blue}{+19x} & = &13 \color{red}{-19x} \color{blue}{+19x} \color{blue}{+35} \\\Leftrightarrow & 20x+19x& = &13+35 \\\Leftrightarrow & 39x& = &48 \\\Leftrightarrow & \frac{39x}{ \color{red}{39} }& = &\frac{48}{ \color{red}{39} } \\\Leftrightarrow & x = \frac{16}{13} & & \\ & V = \left\{ \frac{16}{13} \right\} & \\\end{align}\)