Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-x-7)& = & 9 \color{red}{+} (-12-5x) \\\Leftrightarrow & -6x-42& = &9-12-5x \\\Leftrightarrow & -6x \color{red}{-42} & = &-3 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-42} \color{blue}{+42} \color{blue}{+5x} & = &-3 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+42} \\\Leftrightarrow & -6x+5x& = &-3+42 \\\Leftrightarrow & -x& = &39 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{39}{ \color{red}{-1} } \\\Leftrightarrow & x = -39 & & \\ & V = \left\{ -39 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (3x+7)& = & 11 \color{red}{-} (-15-2x) \\\Leftrightarrow & 15x+35& = &11+15+2x \\\Leftrightarrow & 15x \color{red}{+35} & = &26 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+35} \color{blue}{-35} \color{blue}{-2x} & = &26 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-35} \\\Leftrightarrow & 15x-2x& = &26-35 \\\Leftrightarrow & 13x& = &-9 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-9}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-9}{13} & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-3x+3)& = & -9 \color{red}{+} (3+x) \\\Leftrightarrow & -9x+9& = &-9+3+x \\\Leftrightarrow & -9x \color{red}{+9} & = &-6 \color{red}{+x} \\\Leftrightarrow & -9x \color{red}{+9} \color{blue}{-9} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-9} \\\Leftrightarrow & -9x-x& = &-6-9 \\\Leftrightarrow & -10x& = &-15 \\\Leftrightarrow & \frac{-10x}{ \color{red}{-10} }& = &\frac{-15}{ \color{red}{-10} } \\\Leftrightarrow & x = \frac{3}{2} & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (6x-2)& = & 4 \color{red}{-} (11+x) \\\Leftrightarrow & 12x-4& = &4-11-x \\\Leftrightarrow & 12x \color{red}{-4} & = &-7 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 12x+x& = &-7+4 \\\Leftrightarrow & 13x& = &-3 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-3}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-3}{13} & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-4x-4)& = & 7 \color{red}{+} (7+x) \\\Leftrightarrow & -16x-16& = &7+7+x \\\Leftrightarrow & -16x \color{red}{-16} & = &14 \color{red}{+x} \\\Leftrightarrow & -16x \color{red}{-16} \color{blue}{+16} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{+16} \\\Leftrightarrow & -16x-x& = &14+16 \\\Leftrightarrow & -17x& = &30 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{30}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-30}{17} & & \\ & V = \left\{ \frac{-30}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-5x+6)& = & -6 \color{red}{+} (12-2x) \\\Leftrightarrow & -15x+18& = &-6+12-2x \\\Leftrightarrow & -15x \color{red}{+18} & = &6 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+18} \color{blue}{-18} \color{blue}{+2x} & = &6 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-18} \\\Leftrightarrow & -15x+2x& = &6-18 \\\Leftrightarrow & -13x& = &-12 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-12}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{12}{13} & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-2x-5)& = & 15 \color{red}{+} (-11+x) \\\Leftrightarrow & -6x-15& = &15-11+x \\\Leftrightarrow & -6x \color{red}{-15} & = &4 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & -6x-x& = &4+15 \\\Leftrightarrow & -7x& = &19 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{19}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-19}{7} & & \\ & V = \left\{ \frac{-19}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-4x-1)& = & 5 \color{red}{-} (-9+3x) \\\Leftrightarrow & -16x-4& = &5+9-3x \\\Leftrightarrow & -16x \color{red}{-4} & = &14 \color{red}{-3x} \\\Leftrightarrow & -16x \color{red}{-4} \color{blue}{+4} \color{blue}{+3x} & = &14 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+4} \\\Leftrightarrow & -16x+3x& = &14+4 \\\Leftrightarrow & -13x& = &18 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{18}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-18}{13} & & \\ & V = \left\{ \frac{-18}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (4x+5)& = & -13 \color{red}{+} (-5+x) \\\Leftrightarrow & 12x+15& = &-13-5+x \\\Leftrightarrow & 12x \color{red}{+15} & = &-18 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &-18 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & 12x-x& = &-18-15 \\\Leftrightarrow & 11x& = &-33 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-33}{ \color{red}{11} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (6x-1)& = & 14 \color{red}{-} (-1-5x) \\\Leftrightarrow & 18x-3& = &14+1+5x \\\Leftrightarrow & 18x \color{red}{-3} & = &15 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-3} \color{blue}{+3} \color{blue}{-5x} & = &15 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+3} \\\Leftrightarrow & 18x-5x& = &15+3 \\\Leftrightarrow & 13x& = &18 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{18}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{18}{13} & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (4x+6)& = & -14 \color{red}{+} (-6+x) \\\Leftrightarrow & 20x+30& = &-14-6+x \\\Leftrightarrow & 20x \color{red}{+30} & = &-20 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &-20 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & 20x-x& = &-20-30 \\\Leftrightarrow & 19x& = &-50 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-50}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-50}{19} & & \\ & V = \left\{ \frac{-50}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (4x-6)& = & -1 \color{red}{+} (11+x) \\\Leftrightarrow & 24x-36& = &-1+11+x \\\Leftrightarrow & 24x \color{red}{-36} & = &10 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & 24x-x& = &10+36 \\\Leftrightarrow & 23x& = &46 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{46}{ \color{red}{23} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)