Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-2x+4)& = & -5 \color{red}{-} (2+x) \\\Leftrightarrow & -10x+20& = &-5-2-x \\\Leftrightarrow & -10x \color{red}{+20} & = &-7 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & -10x+x& = &-7-20 \\\Leftrightarrow & -9x& = &-27 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-27}{ \color{red}{-9} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-3x+4)& = & 11 \color{red}{-} (3+x) \\\Leftrightarrow & -6x+8& = &11-3-x \\\Leftrightarrow & -6x \color{red}{+8} & = &8 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -6x+x& = &8-8 \\\Leftrightarrow & -5x& = &0 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{0}{ \color{red}{-5} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-2x-7)& = & -14 \color{red}{-} (-6-5x) \\\Leftrightarrow & -8x-28& = &-14+6+5x \\\Leftrightarrow & -8x \color{red}{-28} & = &-8 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{-28} \color{blue}{+28} \color{blue}{-5x} & = &-8 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+28} \\\Leftrightarrow & -8x-5x& = &-8+28 \\\Leftrightarrow & -13x& = &20 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{20}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-20}{13} & & \\ & V = \left\{ \frac{-20}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (5x-1)& = & 14 \color{red}{-} (9+x) \\\Leftrightarrow & 30x-6& = &14-9-x \\\Leftrightarrow & 30x \color{red}{-6} & = &5 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 30x+x& = &5+6 \\\Leftrightarrow & 31x& = &11 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{11}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{11}{31} & & \\ & V = \left\{ \frac{11}{31} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-4x-2)& = & -9 \color{red}{-} (1+x) \\\Leftrightarrow & -24x-12& = &-9-1-x \\\Leftrightarrow & -24x \color{red}{-12} & = &-10 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -24x+x& = &-10+12 \\\Leftrightarrow & -23x& = &2 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{2}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-2}{23} & & \\ & V = \left\{ \frac{-2}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (2x+2)& = & -11 \color{red}{-} (3-3x) \\\Leftrightarrow & 10x+10& = &-11-3+3x \\\Leftrightarrow & 10x \color{red}{+10} & = &-14 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+10} \color{blue}{-10} \color{blue}{-3x} & = &-14 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-10} \\\Leftrightarrow & 10x-3x& = &-14-10 \\\Leftrightarrow & 7x& = &-24 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-24}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-24}{7} & & \\ & V = \left\{ \frac{-24}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (3x+3)& = & -13 \color{red}{+} (-14+4x) \\\Leftrightarrow & 15x+15& = &-13-14+4x \\\Leftrightarrow & 15x \color{red}{+15} & = &-27 \color{red}{+4x} \\\Leftrightarrow & 15x \color{red}{+15} \color{blue}{-15} \color{blue}{-4x} & = &-27 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-15} \\\Leftrightarrow & 15x-4x& = &-27-15 \\\Leftrightarrow & 11x& = &-42 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-42}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-42}{11} & & \\ & V = \left\{ \frac{-42}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (3x+1)& = & -5 \color{red}{-} (-4+x) \\\Leftrightarrow & 12x+4& = &-5+4-x \\\Leftrightarrow & 12x \color{red}{+4} & = &-1 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 12x+x& = &-1-4 \\\Leftrightarrow & 13x& = &-5 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-5}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-5}{13} & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (3x+2)& = & 13 \color{red}{+} (2-5x) \\\Leftrightarrow & 6x+4& = &13+2-5x \\\Leftrightarrow & 6x \color{red}{+4} & = &15 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+4} \color{blue}{-4} \color{blue}{+5x} & = &15 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-4} \\\Leftrightarrow & 6x+5x& = &15-4 \\\Leftrightarrow & 11x& = &11 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{11}{ \color{red}{11} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (3x+6)& = & -2 \color{red}{-} (3-4x) \\\Leftrightarrow & 9x+18& = &-2-3+4x \\\Leftrightarrow & 9x \color{red}{+18} & = &-5 \color{red}{+4x} \\\Leftrightarrow & 9x \color{red}{+18} \color{blue}{-18} \color{blue}{-4x} & = &-5 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-18} \\\Leftrightarrow & 9x-4x& = &-5-18 \\\Leftrightarrow & 5x& = &-23 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-23}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-23}{5} & & \\ & V = \left\{ \frac{-23}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (5x+2)& = & 3 \color{red}{-} (6+x) \\\Leftrightarrow & 10x+4& = &3-6-x \\\Leftrightarrow & 10x \color{red}{+4} & = &-3 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 10x+x& = &-3-4 \\\Leftrightarrow & 11x& = &-7 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-7}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-7}{11} & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (3x+7)& = & 8 \color{red}{-} (-5-2x) \\\Leftrightarrow & 15x+35& = &8+5+2x \\\Leftrightarrow & 15x \color{red}{+35} & = &13 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+35} \color{blue}{-35} \color{blue}{-2x} & = &13 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-35} \\\Leftrightarrow & 15x-2x& = &13-35 \\\Leftrightarrow & 13x& = &-22 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-22}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-22}{13} & & \\ & V = \left\{ \frac{-22}{13} \right\} & \\\end{align}\)