Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(2(-2x+7)=-2+(8-3x)\)
2. \(4(3x+3)=-15+(6+x)\)
3. \(5(6x+7)=12+(-6+x)\)
4. \(2(6x-4)=3+(12+5x)\)
5. \(3(-6x-3)=11+(13+x)\)
6. \(2(4x+5)=11-(13-5x)\)
7. \(4(-x-4)=-11-(-3-3x)\)
8. \(5(x+2)=-12+(12+x)\)
9. \(2(5x-3)=-4+(15+x)\)
10. \(3(6x+7)=5-(-10+x)\)
11. \(6(6x+1)=-8-(-5+35x)\)
12. \(4(-4x-1)=10-(-15-3x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-2x+7)& = & -2 \color{red}{+} (8-3x) \\\Leftrightarrow & -4x+14& = &-2+8-3x \\\Leftrightarrow & -4x \color{red}{+14} & = &6 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+14} \color{blue}{-14} \color{blue}{+3x} & = &6 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-14} \\\Leftrightarrow & -4x+3x& = &6-14 \\\Leftrightarrow & -x& = &-8 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-8}{ \color{red}{-1} } \\\Leftrightarrow & x = 8 & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (3x+3)& = & -15 \color{red}{+} (6+x) \\\Leftrightarrow & 12x+12& = &-15+6+x \\\Leftrightarrow & 12x \color{red}{+12} & = &-9 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 12x-x& = &-9-12 \\\Leftrightarrow & 11x& = &-21 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-21}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-21}{11} & & \\ & V = \left\{ \frac{-21}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (6x+7)& = & 12 \color{red}{+} (-6+x) \\\Leftrightarrow & 30x+35& = &12-6+x \\\Leftrightarrow & 30x \color{red}{+35} & = &6 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+35} \color{blue}{-35} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{-35} \\\Leftrightarrow & 30x-x& = &6-35 \\\Leftrightarrow & 29x& = &-29 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-29}{ \color{red}{29} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (6x-4)& = & 3 \color{red}{+} (12+5x) \\\Leftrightarrow & 12x-8& = &3+12+5x \\\Leftrightarrow & 12x \color{red}{-8} & = &15 \color{red}{+5x} \\\Leftrightarrow & 12x \color{red}{-8} \color{blue}{+8} \color{blue}{-5x} & = &15 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+8} \\\Leftrightarrow & 12x-5x& = &15+8 \\\Leftrightarrow & 7x& = &23 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{23}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{23}{7} & & \\ & V = \left\{ \frac{23}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-6x-3)& = & 11 \color{red}{+} (13+x) \\\Leftrightarrow & -18x-9& = &11+13+x \\\Leftrightarrow & -18x \color{red}{-9} & = &24 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-9} \color{blue}{+9} \color{blue}{-x} & = &24 \color{red}{+x} \color{blue}{-x} \color{blue}{+9} \\\Leftrightarrow & -18x-x& = &24+9 \\\Leftrightarrow & -19x& = &33 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{33}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-33}{19} & & \\ & V = \left\{ \frac{-33}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (4x+5)& = & 11 \color{red}{-} (13-5x) \\\Leftrightarrow & 8x+10& = &11-13+5x \\\Leftrightarrow & 8x \color{red}{+10} & = &-2 \color{red}{+5x} \\\Leftrightarrow & 8x \color{red}{+10} \color{blue}{-10} \color{blue}{-5x} & = &-2 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-10} \\\Leftrightarrow & 8x-5x& = &-2-10 \\\Leftrightarrow & 3x& = &-12 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-12}{ \color{red}{3} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-x-4)& = & -11 \color{red}{-} (-3-3x) \\\Leftrightarrow & -4x-16& = &-11+3+3x \\\Leftrightarrow & -4x \color{red}{-16} & = &-8 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-16} \color{blue}{+16} \color{blue}{-3x} & = &-8 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+16} \\\Leftrightarrow & -4x-3x& = &-8+16 \\\Leftrightarrow & -7x& = &8 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{8}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-8}{7} & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (x+2)& = & -12 \color{red}{+} (12+x) \\\Leftrightarrow & 5x+10& = &-12+12+x \\\Leftrightarrow & 5x \color{red}{+10} & = &0 \color{red}{+x} \\\Leftrightarrow & 5x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & 5x-x& = &0-10 \\\Leftrightarrow & 4x& = &-10 \\\Leftrightarrow & \frac{4x}{ \color{red}{4} }& = &\frac{-10}{ \color{red}{4} } \\\Leftrightarrow & x = \frac{-5}{2} & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (5x-3)& = & -4 \color{red}{+} (15+x) \\\Leftrightarrow & 10x-6& = &-4+15+x \\\Leftrightarrow & 10x \color{red}{-6} & = &11 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 10x-x& = &11+6 \\\Leftrightarrow & 9x& = &17 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{17}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{17}{9} & & \\ & V = \left\{ \frac{17}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (6x+7)& = & 5 \color{red}{-} (-10+x) \\\Leftrightarrow & 18x+21& = &5+10-x \\\Leftrightarrow & 18x \color{red}{+21} & = &15 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+21} \color{blue}{-21} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{-21} \\\Leftrightarrow & 18x+x& = &15-21 \\\Leftrightarrow & 19x& = &-6 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-6}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-6}{19} & & \\ & V = \left\{ \frac{-6}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (6x+1)& = & -8 \color{red}{-} (-5+35x) \\\Leftrightarrow & 36x+6& = &-8+5-35x \\\Leftrightarrow & 36x \color{red}{+6} & = &-3 \color{red}{-35x} \\\Leftrightarrow & 36x \color{red}{+6} \color{blue}{-6} \color{blue}{+35x} & = &-3 \color{red}{-35x} \color{blue}{+35x} \color{blue}{-6} \\\Leftrightarrow & 36x+35x& = &-3-6 \\\Leftrightarrow & 71x& = &-9 \\\Leftrightarrow & \frac{71x}{ \color{red}{71} }& = &\frac{-9}{ \color{red}{71} } \\\Leftrightarrow & x = \frac{-9}{71} & & \\ & V = \left\{ \frac{-9}{71} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-4x-1)& = & 10 \color{red}{-} (-15-3x) \\\Leftrightarrow & -16x-4& = &10+15+3x \\\Leftrightarrow & -16x \color{red}{-4} & = &25 \color{red}{+3x} \\\Leftrightarrow & -16x \color{red}{-4} \color{blue}{+4} \color{blue}{-3x} & = &25 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+4} \\\Leftrightarrow & -16x-3x& = &25+4 \\\Leftrightarrow & -19x& = &29 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{29}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-29}{19} & & \\ & V = \left\{ \frac{-29}{19} \right\} & \\\end{align}\)