Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-x-1)& = & 9 \color{red}{-} (-5+x) \\\Leftrightarrow & -6x-6& = &9+5-x \\\Leftrightarrow & -6x \color{red}{-6} & = &14 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -6x+x& = &14+6 \\\Leftrightarrow & -5x& = &20 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{20}{ \color{red}{-5} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (3x-7)& = & -11 \color{red}{-} (-6+x) \\\Leftrightarrow & 18x-42& = &-11+6-x \\\Leftrightarrow & 18x \color{red}{-42} & = &-5 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & 18x+x& = &-5+42 \\\Leftrightarrow & 19x& = &37 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{37}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{37}{19} & & \\ & V = \left\{ \frac{37}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-3x+6)& = & 9 \color{red}{+} (-15+x) \\\Leftrightarrow & -12x+24& = &9-15+x \\\Leftrightarrow & -12x \color{red}{+24} & = &-6 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -12x-x& = &-6-24 \\\Leftrightarrow & -13x& = &-30 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-30}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{30}{13} & & \\ & V = \left\{ \frac{30}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-x+5)& = & -8 \color{red}{+} (15+4x) \\\Leftrightarrow & -3x+15& = &-8+15+4x \\\Leftrightarrow & -3x \color{red}{+15} & = &7 \color{red}{+4x} \\\Leftrightarrow & -3x \color{red}{+15} \color{blue}{-15} \color{blue}{-4x} & = &7 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-15} \\\Leftrightarrow & -3x-4x& = &7-15 \\\Leftrightarrow & -7x& = &-8 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-8}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{8}{7} & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (2x+4)& = & -12 \color{red}{-} (2+x) \\\Leftrightarrow & 6x+12& = &-12-2-x \\\Leftrightarrow & 6x \color{red}{+12} & = &-14 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 6x+x& = &-14-12 \\\Leftrightarrow & 7x& = &-26 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-26}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-26}{7} & & \\ & V = \left\{ \frac{-26}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-4x-5)& = & 5 \color{red}{-} (-9+x) \\\Leftrightarrow & -24x-30& = &5+9-x \\\Leftrightarrow & -24x \color{red}{-30} & = &14 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & -24x+x& = &14+30 \\\Leftrightarrow & -23x& = &44 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{44}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-44}{23} & & \\ & V = \left\{ \frac{-44}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-4x-5)& = & -13 \color{red}{-} (-6+x) \\\Leftrightarrow & -8x-10& = &-13+6-x \\\Leftrightarrow & -8x \color{red}{-10} & = &-7 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & -8x+x& = &-7+10 \\\Leftrightarrow & -7x& = &3 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{3}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-3}{7} & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-3x+7)& = & -5 \color{red}{-} (8+4x) \\\Leftrightarrow & -15x+35& = &-5-8-4x \\\Leftrightarrow & -15x \color{red}{+35} & = &-13 \color{red}{-4x} \\\Leftrightarrow & -15x \color{red}{+35} \color{blue}{-35} \color{blue}{+4x} & = &-13 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-35} \\\Leftrightarrow & -15x+4x& = &-13-35 \\\Leftrightarrow & -11x& = &-48 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-48}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{48}{11} & & \\ & V = \left\{ \frac{48}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-4x+7)& = & 13 \color{red}{+} (-4+x) \\\Leftrightarrow & -24x+42& = &13-4+x \\\Leftrightarrow & -24x \color{red}{+42} & = &9 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & -24x-x& = &9-42 \\\Leftrightarrow & -25x& = &-33 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-33}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{33}{25} & & \\ & V = \left\{ \frac{33}{25} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-3x-3)& = & 6 \color{red}{-} (9+x) \\\Leftrightarrow & -12x-12& = &6-9-x \\\Leftrightarrow & -12x \color{red}{-12} & = &-3 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -12x+x& = &-3+12 \\\Leftrightarrow & -11x& = &9 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{9}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-9}{11} & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (3x+4)& = & 15 \color{red}{+} (7-2x) \\\Leftrightarrow & 15x+20& = &15+7-2x \\\Leftrightarrow & 15x \color{red}{+20} & = &22 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{+20} \color{blue}{-20} \color{blue}{+2x} & = &22 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-20} \\\Leftrightarrow & 15x+2x& = &22-20 \\\Leftrightarrow & 17x& = &2 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{2}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{2}{17} & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-x-4)& = & 10 \color{red}{+} (-9+x) \\\Leftrightarrow & -4x-16& = &10-9+x \\\Leftrightarrow & -4x \color{red}{-16} & = &1 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{-16} \color{blue}{+16} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+16} \\\Leftrightarrow & -4x-x& = &1+16 \\\Leftrightarrow & -5x& = &17 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{17}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-17}{5} & & \\ & V = \left\{ \frac{-17}{5} \right\} & \\\end{align}\)