Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-4x+5)& = & -9 \color{red}{-} (4+x) \\\Leftrightarrow & -12x+15& = &-9-4-x \\\Leftrightarrow & -12x \color{red}{+15} & = &-13 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & -12x+x& = &-13-15 \\\Leftrightarrow & -11x& = &-28 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-28}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{28}{11} & & \\ & V = \left\{ \frac{28}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (2x-7)& = & -2 \color{red}{-} (9+3x) \\\Leftrightarrow & 8x-28& = &-2-9-3x \\\Leftrightarrow & 8x \color{red}{-28} & = &-11 \color{red}{-3x} \\\Leftrightarrow & 8x \color{red}{-28} \color{blue}{+28} \color{blue}{+3x} & = &-11 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+28} \\\Leftrightarrow & 8x+3x& = &-11+28 \\\Leftrightarrow & 11x& = &17 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{17}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{17}{11} & & \\ & V = \left\{ \frac{17}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-2x+2)& = & -1 \color{red}{+} (9-3x) \\\Leftrightarrow & -4x+4& = &-1+9-3x \\\Leftrightarrow & -4x \color{red}{+4} & = &8 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+4} \color{blue}{-4} \color{blue}{+3x} & = &8 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-4} \\\Leftrightarrow & -4x+3x& = &8-4 \\\Leftrightarrow & -x& = &4 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{4}{ \color{red}{-1} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-4x-5)& = & -3 \color{red}{-} (-8+3x) \\\Leftrightarrow & -8x-10& = &-3+8-3x \\\Leftrightarrow & -8x \color{red}{-10} & = &5 \color{red}{-3x} \\\Leftrightarrow & -8x \color{red}{-10} \color{blue}{+10} \color{blue}{+3x} & = &5 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+10} \\\Leftrightarrow & -8x+3x& = &5+10 \\\Leftrightarrow & -5x& = &15 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{15}{ \color{red}{-5} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-6x+5)& = & -7 \color{red}{-} (-15+x) \\\Leftrightarrow & -12x+10& = &-7+15-x \\\Leftrightarrow & -12x \color{red}{+10} & = &8 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & -12x+x& = &8-10 \\\Leftrightarrow & -11x& = &-2 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-2}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{2}{11} & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (3x-4)& = & 14 \color{red}{+} (7-4x) \\\Leftrightarrow & 9x-12& = &14+7-4x \\\Leftrightarrow & 9x \color{red}{-12} & = &21 \color{red}{-4x} \\\Leftrightarrow & 9x \color{red}{-12} \color{blue}{+12} \color{blue}{+4x} & = &21 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+12} \\\Leftrightarrow & 9x+4x& = &21+12 \\\Leftrightarrow & 13x& = &33 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{33}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{33}{13} & & \\ & V = \left\{ \frac{33}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-4x+7)& = & -12 \color{red}{-} (6+x) \\\Leftrightarrow & -8x+14& = &-12-6-x \\\Leftrightarrow & -8x \color{red}{+14} & = &-18 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+14} \color{blue}{-14} \color{blue}{+x} & = &-18 \color{red}{-x} \color{blue}{+x} \color{blue}{-14} \\\Leftrightarrow & -8x+x& = &-18-14 \\\Leftrightarrow & -7x& = &-32 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-32}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{32}{7} & & \\ & V = \left\{ \frac{32}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-5x-1)& = & 3 \color{red}{-} (-4+x) \\\Leftrightarrow & -20x-4& = &3+4-x \\\Leftrightarrow & -20x \color{red}{-4} & = &7 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & -20x+x& = &7+4 \\\Leftrightarrow & -19x& = &11 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{11}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-11}{19} & & \\ & V = \left\{ \frac{-11}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (2x-6)& = & 5 \color{red}{+} (-15+x) \\\Leftrightarrow & 4x-12& = &5-15+x \\\Leftrightarrow & 4x \color{red}{-12} & = &-10 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 4x-x& = &-10+12 \\\Leftrightarrow & 3x& = &2 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{2}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{2}{3} & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (6x-7)& = & 14 \color{red}{-} (11+x) \\\Leftrightarrow & 36x-42& = &14-11-x \\\Leftrightarrow & 36x \color{red}{-42} & = &3 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & 36x+x& = &3+42 \\\Leftrightarrow & 37x& = &45 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{45}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{45}{37} & & \\ & V = \left\{ \frac{45}{37} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (3x+1)& = & -4 \color{red}{-} (-8+4x) \\\Leftrightarrow & 9x+3& = &-4+8-4x \\\Leftrightarrow & 9x \color{red}{+3} & = &4 \color{red}{-4x} \\\Leftrightarrow & 9x \color{red}{+3} \color{blue}{-3} \color{blue}{+4x} & = &4 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-3} \\\Leftrightarrow & 9x+4x& = &4-3 \\\Leftrightarrow & 13x& = &1 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{1}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{1}{13} & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (3x+1)& = & 1 \color{red}{-} (-5-2x) \\\Leftrightarrow & 15x+5& = &1+5+2x \\\Leftrightarrow & 15x \color{red}{+5} & = &6 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+5} \color{blue}{-5} \color{blue}{-2x} & = &6 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-5} \\\Leftrightarrow & 15x-2x& = &6-5 \\\Leftrightarrow & 13x& = &1 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{1}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{1}{13} & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)