Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-x+2)& = & -3 \color{red}{+} (-4+x) \\\Leftrightarrow & -2x+4& = &-3-4+x \\\Leftrightarrow & -2x \color{red}{+4} & = &-7 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & -2x-x& = &-7-4 \\\Leftrightarrow & -3x& = &-11 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-11}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{11}{3} & & \\ & V = \left\{ \frac{11}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (4x+7)& = & -1 \color{red}{+} (7+3x) \\\Leftrightarrow & 20x+35& = &-1+7+3x \\\Leftrightarrow & 20x \color{red}{+35} & = &6 \color{red}{+3x} \\\Leftrightarrow & 20x \color{red}{+35} \color{blue}{-35} \color{blue}{-3x} & = &6 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-35} \\\Leftrightarrow & 20x-3x& = &6-35 \\\Leftrightarrow & 17x& = &-29 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-29}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-29}{17} & & \\ & V = \left\{ \frac{-29}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (5x+5)& = & 10 \color{red}{-} (-13+4x) \\\Leftrightarrow & 15x+15& = &10+13-4x \\\Leftrightarrow & 15x \color{red}{+15} & = &23 \color{red}{-4x} \\\Leftrightarrow & 15x \color{red}{+15} \color{blue}{-15} \color{blue}{+4x} & = &23 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-15} \\\Leftrightarrow & 15x+4x& = &23-15 \\\Leftrightarrow & 19x& = &8 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{8}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{8}{19} & & \\ & V = \left\{ \frac{8}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (3x-2)& = & 15 \color{red}{+} (12-4x) \\\Leftrightarrow & 9x-6& = &15+12-4x \\\Leftrightarrow & 9x \color{red}{-6} & = &27 \color{red}{-4x} \\\Leftrightarrow & 9x \color{red}{-6} \color{blue}{+6} \color{blue}{+4x} & = &27 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+6} \\\Leftrightarrow & 9x+4x& = &27+6 \\\Leftrightarrow & 13x& = &33 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{33}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{33}{13} & & \\ & V = \left\{ \frac{33}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (2x+5)& = & -1 \color{red}{+} (8+x) \\\Leftrightarrow & 10x+25& = &-1+8+x \\\Leftrightarrow & 10x \color{red}{+25} & = &7 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{+25} \color{blue}{-25} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{-25} \\\Leftrightarrow & 10x-x& = &7-25 \\\Leftrightarrow & 9x& = &-18 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-18}{ \color{red}{9} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-2x+7)& = & 7 \color{red}{+} (3+x) \\\Leftrightarrow & -10x+35& = &7+3+x \\\Leftrightarrow & -10x \color{red}{+35} & = &10 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{+35} \color{blue}{-35} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{-35} \\\Leftrightarrow & -10x-x& = &10-35 \\\Leftrightarrow & -11x& = &-25 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-25}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{25}{11} & & \\ & V = \left\{ \frac{25}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (3x+2)& = & 6 \color{red}{+} (-1+x) \\\Leftrightarrow & 9x+6& = &6-1+x \\\Leftrightarrow & 9x \color{red}{+6} & = &5 \color{red}{+x} \\\Leftrightarrow & 9x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 9x-x& = &5-6 \\\Leftrightarrow & 8x& = &-1 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{-1}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{-1}{8} & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (6x+2)& = & 2 \color{red}{+} (-6-5x) \\\Leftrightarrow & 18x+6& = &2-6-5x \\\Leftrightarrow & 18x \color{red}{+6} & = &-4 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &-4 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & 18x+5x& = &-4-6 \\\Leftrightarrow & 23x& = &-10 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-10}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-10}{23} & & \\ & V = \left\{ \frac{-10}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-6x-7)& = & -3 \color{red}{+} (3+x) \\\Leftrightarrow & -36x-42& = &-3+3+x \\\Leftrightarrow & -36x \color{red}{-42} & = &0 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & -36x-x& = &0+42 \\\Leftrightarrow & -37x& = &42 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{42}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{-42}{37} & & \\ & V = \left\{ \frac{-42}{37} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-4x-4)& = & 13 \color{red}{+} (-8-3x) \\\Leftrightarrow & -16x-16& = &13-8-3x \\\Leftrightarrow & -16x \color{red}{-16} & = &5 \color{red}{-3x} \\\Leftrightarrow & -16x \color{red}{-16} \color{blue}{+16} \color{blue}{+3x} & = &5 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+16} \\\Leftrightarrow & -16x+3x& = &5+16 \\\Leftrightarrow & -13x& = &21 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{21}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-21}{13} & & \\ & V = \left\{ \frac{-21}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-3x-6)& = & -12 \color{red}{-} (9+x) \\\Leftrightarrow & -6x-12& = &-12-9-x \\\Leftrightarrow & -6x \color{red}{-12} & = &-21 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-21 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -6x+x& = &-21+12 \\\Leftrightarrow & -5x& = &-9 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-9}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{9}{5} & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (3x-6)& = & -8 \color{red}{+} (-14+x) \\\Leftrightarrow & 18x-36& = &-8-14+x \\\Leftrightarrow & 18x \color{red}{-36} & = &-22 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &-22 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & 18x-x& = &-22+36 \\\Leftrightarrow & 17x& = &14 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{14}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{14}{17} & & \\ & V = \left\{ \frac{14}{17} \right\} & \\\end{align}\)