Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (2x-7)& = & 4 \color{red}{+} (-6+x) \\\Leftrightarrow & 12x-42& = &4-6+x \\\Leftrightarrow & 12x \color{red}{-42} & = &-2 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & 12x-x& = &-2+42 \\\Leftrightarrow & 11x& = &40 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{40}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{40}{11} & & \\ & V = \left\{ \frac{40}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (x+7)& = & 5 \color{red}{-} (-6+x) \\\Leftrightarrow & 2x+14& = &5+6-x \\\Leftrightarrow & 2x \color{red}{+14} & = &11 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{+14} \color{blue}{-14} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{-14} \\\Leftrightarrow & 2x+x& = &11-14 \\\Leftrightarrow & 3x& = &-3 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-3}{ \color{red}{3} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (5x-7)& = & 2 \color{red}{-} (2+3x) \\\Leftrightarrow & 10x-14& = &2-2-3x \\\Leftrightarrow & 10x \color{red}{-14} & = &0 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-14} \color{blue}{+14} \color{blue}{+3x} & = &0 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+14} \\\Leftrightarrow & 10x+3x& = &0+14 \\\Leftrightarrow & 13x& = &14 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{14}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{14}{13} & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (6x+1)& = & 10 \color{red}{+} (-6+x) \\\Leftrightarrow & 12x+2& = &10-6+x \\\Leftrightarrow & 12x \color{red}{+2} & = &4 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+2} \color{blue}{-2} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{-2} \\\Leftrightarrow & 12x-x& = &4-2 \\\Leftrightarrow & 11x& = &2 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{2}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{2}{11} & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (3x+3)& = & 15 \color{red}{+} (-14-5x) \\\Leftrightarrow & 18x+18& = &15-14-5x \\\Leftrightarrow & 18x \color{red}{+18} & = &1 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{+18} \color{blue}{-18} \color{blue}{+5x} & = &1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-18} \\\Leftrightarrow & 18x+5x& = &1-18 \\\Leftrightarrow & 23x& = &-17 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-17}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-17}{23} & & \\ & V = \left\{ \frac{-17}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-6x-2)& = & 1 \color{red}{-} (-3+x) \\\Leftrightarrow & -12x-4& = &1+3-x \\\Leftrightarrow & -12x \color{red}{-4} & = &4 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & -12x+x& = &4+4 \\\Leftrightarrow & -11x& = &8 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{8}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-8}{11} & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-4x-6)& = & -4 \color{red}{+} (-6+x) \\\Leftrightarrow & -12x-18& = &-4-6+x \\\Leftrightarrow & -12x \color{red}{-18} & = &-10 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & -12x-x& = &-10+18 \\\Leftrightarrow & -13x& = &8 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{8}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-8}{13} & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (6x+5)& = & -3 \color{red}{-} (8+x) \\\Leftrightarrow & 18x+15& = &-3-8-x \\\Leftrightarrow & 18x \color{red}{+15} & = &-11 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & 18x+x& = &-11-15 \\\Leftrightarrow & 19x& = &-26 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-26}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-26}{19} & & \\ & V = \left\{ \frac{-26}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-x+2)& = & -7 \color{red}{-} (-11-3x) \\\Leftrightarrow & -4x+8& = &-7+11+3x \\\Leftrightarrow & -4x \color{red}{+8} & = &4 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+8} \color{blue}{-8} \color{blue}{-3x} & = &4 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-8} \\\Leftrightarrow & -4x-3x& = &4-8 \\\Leftrightarrow & -7x& = &-4 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-4}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{4}{7} & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (2x+4)& = & 9 \color{red}{+} (-9-5x) \\\Leftrightarrow & 6x+12& = &9-9-5x \\\Leftrightarrow & 6x \color{red}{+12} & = &0 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+12} \color{blue}{-12} \color{blue}{+5x} & = &0 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-12} \\\Leftrightarrow & 6x+5x& = &0-12 \\\Leftrightarrow & 11x& = &-12 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-12}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-12}{11} & & \\ & V = \left\{ \frac{-12}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (4x+2)& = & -8 \color{red}{+} (-12+x) \\\Leftrightarrow & 16x+8& = &-8-12+x \\\Leftrightarrow & 16x \color{red}{+8} & = &-20 \color{red}{+x} \\\Leftrightarrow & 16x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-20 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 16x-x& = &-20-8 \\\Leftrightarrow & 15x& = &-28 \\\Leftrightarrow & \frac{15x}{ \color{red}{15} }& = &\frac{-28}{ \color{red}{15} } \\\Leftrightarrow & x = \frac{-28}{15} & & \\ & V = \left\{ \frac{-28}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-x-2)& = & -13 \color{red}{-} (4+3x) \\\Leftrightarrow & -2x-4& = &-13-4-3x \\\Leftrightarrow & -2x \color{red}{-4} & = &-17 \color{red}{-3x} \\\Leftrightarrow & -2x \color{red}{-4} \color{blue}{+4} \color{blue}{+3x} & = &-17 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+4} \\\Leftrightarrow & -2x+3x& = &-17+4 \\\Leftrightarrow & x& = &-13 \\ & V = \left\{ -13 \right\} & \\\end{align}\)