Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (4x-3)& = & -6 \color{red}{+} (-1+x) \\\Leftrightarrow & 20x-15& = &-6-1+x \\\Leftrightarrow & 20x \color{red}{-15} & = &-7 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & 20x-x& = &-7+15 \\\Leftrightarrow & 19x& = &8 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{8}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{8}{19} & & \\ & V = \left\{ \frac{8}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-6x-2)& = & -8 \color{red}{-} (15+x) \\\Leftrightarrow & -18x-6& = &-8-15-x \\\Leftrightarrow & -18x \color{red}{-6} & = &-23 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-23 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -18x+x& = &-23+6 \\\Leftrightarrow & -17x& = &-17 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-17}{ \color{red}{-17} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (4x+6)& = & 9 \color{red}{-} (8+x) \\\Leftrightarrow & 24x+36& = &9-8-x \\\Leftrightarrow & 24x \color{red}{+36} & = &1 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & 24x+x& = &1-36 \\\Leftrightarrow & 25x& = &-35 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-35}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-7}{5} & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (2x+2)& = & 14 \color{red}{-} (11+x) \\\Leftrightarrow & 6x+6& = &14-11-x \\\Leftrightarrow & 6x \color{red}{+6} & = &3 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 6x+x& = &3-6 \\\Leftrightarrow & 7x& = &-3 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-3}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-3}{7} & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (2x+6)& = & 8 \color{red}{+} (-4+x) \\\Leftrightarrow & 12x+36& = &8-4+x \\\Leftrightarrow & 12x \color{red}{+36} & = &4 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & 12x-x& = &4-36 \\\Leftrightarrow & 11x& = &-32 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-32}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-32}{11} & & \\ & V = \left\{ \frac{-32}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (x-7)& = & -5 \color{red}{+} (-5-4x) \\\Leftrightarrow & 5x-35& = &-5-5-4x \\\Leftrightarrow & 5x \color{red}{-35} & = &-10 \color{red}{-4x} \\\Leftrightarrow & 5x \color{red}{-35} \color{blue}{+35} \color{blue}{+4x} & = &-10 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+35} \\\Leftrightarrow & 5x+4x& = &-10+35 \\\Leftrightarrow & 9x& = &25 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{25}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{25}{9} & & \\ & V = \left\{ \frac{25}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-x-1)& = & 13 \color{red}{+} (2-3x) \\\Leftrightarrow & -4x-4& = &13+2-3x \\\Leftrightarrow & -4x \color{red}{-4} & = &15 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-4} \color{blue}{+4} \color{blue}{+3x} & = &15 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+4} \\\Leftrightarrow & -4x+3x& = &15+4 \\\Leftrightarrow & -x& = &19 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{19}{ \color{red}{-1} } \\\Leftrightarrow & x = -19 & & \\ & V = \left\{ -19 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (x+2)& = & -14 \color{red}{+} (14+x) \\\Leftrightarrow & 2x+4& = &-14+14+x \\\Leftrightarrow & 2x \color{red}{+4} & = &0 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 2x-x& = &0-4 \\\Leftrightarrow & x& = &-4 \\ & V = \left\{ -4 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-2x+3)& = & 15 \color{red}{-} (-15-3x) \\\Leftrightarrow & -4x+6& = &15+15+3x \\\Leftrightarrow & -4x \color{red}{+6} & = &30 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+6} \color{blue}{-6} \color{blue}{-3x} & = &30 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-6} \\\Leftrightarrow & -4x-3x& = &30-6 \\\Leftrightarrow & -7x& = &24 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{24}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-24}{7} & & \\ & V = \left\{ \frac{-24}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-2x-2)& = & 7 \color{red}{+} (-7+x) \\\Leftrightarrow & -12x-12& = &7-7+x \\\Leftrightarrow & -12x \color{red}{-12} & = &0 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -12x-x& = &0+12 \\\Leftrightarrow & -13x& = &12 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{12}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-12}{13} & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-5x-2)& = & -6 \color{red}{+} (7-2x) \\\Leftrightarrow & -25x-10& = &-6+7-2x \\\Leftrightarrow & -25x \color{red}{-10} & = &1 \color{red}{-2x} \\\Leftrightarrow & -25x \color{red}{-10} \color{blue}{+10} \color{blue}{+2x} & = &1 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+10} \\\Leftrightarrow & -25x+2x& = &1+10 \\\Leftrightarrow & -23x& = &11 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{11}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-11}{23} & & \\ & V = \left\{ \frac{-11}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-2x+6)& = & 5 \color{red}{-} (6+x) \\\Leftrightarrow & -6x+18& = &5-6-x \\\Leftrightarrow & -6x \color{red}{+18} & = &-1 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -6x+x& = &-1-18 \\\Leftrightarrow & -5x& = &-19 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-19}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{19}{5} & & \\ & V = \left\{ \frac{19}{5} \right\} & \\\end{align}\)