Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (6x+5)& = & 8 \color{red}{+} (11+x) \\\Leftrightarrow & 30x+25& = &8+11+x \\\Leftrightarrow & 30x \color{red}{+25} & = &19 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+25} \color{blue}{-25} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{-25} \\\Leftrightarrow & 30x-x& = &19-25 \\\Leftrightarrow & 29x& = &-6 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-6}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-6}{29} & & \\ & V = \left\{ \frac{-6}{29} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (4x+1)& = & 3 \color{red}{+} (8+x) \\\Leftrightarrow & 12x+3& = &3+8+x \\\Leftrightarrow & 12x \color{red}{+3} & = &11 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & 12x-x& = &11-3 \\\Leftrightarrow & 11x& = &8 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{8}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{8}{11} & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (3x-7)& = & 3 \color{red}{-} (5-2x) \\\Leftrightarrow & 15x-35& = &3-5+2x \\\Leftrightarrow & 15x \color{red}{-35} & = &-2 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{-35} \color{blue}{+35} \color{blue}{-2x} & = &-2 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+35} \\\Leftrightarrow & 15x-2x& = &-2+35 \\\Leftrightarrow & 13x& = &33 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{33}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{33}{13} & & \\ & V = \left\{ \frac{33}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (5x+7)& = & 15 \color{red}{-} (2-2x) \\\Leftrightarrow & 15x+21& = &15-2+2x \\\Leftrightarrow & 15x \color{red}{+21} & = &13 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+21} \color{blue}{-21} \color{blue}{-2x} & = &13 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-21} \\\Leftrightarrow & 15x-2x& = &13-21 \\\Leftrightarrow & 13x& = &-8 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-8}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-8}{13} & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (3x+5)& = & -2 \color{red}{+} (-12+x) \\\Leftrightarrow & 6x+10& = &-2-12+x \\\Leftrightarrow & 6x \color{red}{+10} & = &-14 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & 6x-x& = &-14-10 \\\Leftrightarrow & 5x& = &-24 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-24}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-24}{5} & & \\ & V = \left\{ \frac{-24}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-5x+4)& = & 10 \color{red}{-} (2-3x) \\\Leftrightarrow & -10x+8& = &10-2+3x \\\Leftrightarrow & -10x \color{red}{+8} & = &8 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+8} \color{blue}{-8} \color{blue}{-3x} & = &8 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-8} \\\Leftrightarrow & -10x-3x& = &8-8 \\\Leftrightarrow & -13x& = &0 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{0}{ \color{red}{-13} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (2x-1)& = & -10 \color{red}{+} (-10-3x) \\\Leftrightarrow & 10x-5& = &-10-10-3x \\\Leftrightarrow & 10x \color{red}{-5} & = &-20 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-5} \color{blue}{+5} \color{blue}{+3x} & = &-20 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+5} \\\Leftrightarrow & 10x+3x& = &-20+5 \\\Leftrightarrow & 13x& = &-15 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-15}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-15}{13} & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-x-1)& = & 8 \color{red}{+} (10+x) \\\Leftrightarrow & -6x-6& = &8+10+x \\\Leftrightarrow & -6x \color{red}{-6} & = &18 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &18 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -6x-x& = &18+6 \\\Leftrightarrow & -7x& = &24 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{24}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-24}{7} & & \\ & V = \left\{ \frac{-24}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-x+3)& = & 13 \color{red}{-} (-11+x) \\\Leftrightarrow & -5x+15& = &13+11-x \\\Leftrightarrow & -5x \color{red}{+15} & = &24 \color{red}{-x} \\\Leftrightarrow & -5x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &24 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & -5x+x& = &24-15 \\\Leftrightarrow & -4x& = &9 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{9}{ \color{red}{-4} } \\\Leftrightarrow & x = \frac{-9}{4} & & \\ & V = \left\{ \frac{-9}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-x-4)& = & -5 \color{red}{+} (1+x) \\\Leftrightarrow & -3x-12& = &-5+1+x \\\Leftrightarrow & -3x \color{red}{-12} & = &-4 \color{red}{+x} \\\Leftrightarrow & -3x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -3x-x& = &-4+12 \\\Leftrightarrow & -4x& = &8 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{8}{ \color{red}{-4} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (3x-7)& = & 1 \color{red}{+} (-5-5x) \\\Leftrightarrow & 18x-42& = &1-5-5x \\\Leftrightarrow & 18x \color{red}{-42} & = &-4 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-42} \color{blue}{+42} \color{blue}{+5x} & = &-4 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+42} \\\Leftrightarrow & 18x+5x& = &-4+42 \\\Leftrightarrow & 23x& = &38 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{38}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{38}{23} & & \\ & V = \left\{ \frac{38}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-2x-3)& = & -15 \color{red}{-} (-7+x) \\\Leftrightarrow & -12x-18& = &-15+7-x \\\Leftrightarrow & -12x \color{red}{-18} & = &-8 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & -12x+x& = &-8+18 \\\Leftrightarrow & -11x& = &10 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{10}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-10}{11} & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)