Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (5x-1)& = & -15 \color{red}{-} (4+x) \\\Leftrightarrow & 20x-4& = &-15-4-x \\\Leftrightarrow & 20x \color{red}{-4} & = &-19 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 20x+x& = &-19+4 \\\Leftrightarrow & 21x& = &-15 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-15}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-5}{7} & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-3x+4)& = & 6 \color{red}{+} (-6-5x) \\\Leftrightarrow & -6x+8& = &6-6-5x \\\Leftrightarrow & -6x \color{red}{+8} & = &0 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+8} \color{blue}{-8} \color{blue}{+5x} & = &0 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-8} \\\Leftrightarrow & -6x+5x& = &0-8 \\\Leftrightarrow & -x& = &-8 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-8}{ \color{red}{-1} } \\\Leftrightarrow & x = 8 & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (x-1)& = & -4 \color{red}{+} (-13+x) \\\Leftrightarrow & 6x-6& = &-4-13+x \\\Leftrightarrow & 6x \color{red}{-6} & = &-17 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 6x-x& = &-17+6 \\\Leftrightarrow & 5x& = &-11 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-11}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-11}{5} & & \\ & V = \left\{ \frac{-11}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (4x-3)& = & 9 \color{red}{-} (-12+3x) \\\Leftrightarrow & 20x-15& = &9+12-3x \\\Leftrightarrow & 20x \color{red}{-15} & = &21 \color{red}{-3x} \\\Leftrightarrow & 20x \color{red}{-15} \color{blue}{+15} \color{blue}{+3x} & = &21 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+15} \\\Leftrightarrow & 20x+3x& = &21+15 \\\Leftrightarrow & 23x& = &36 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{36}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{36}{23} & & \\ & V = \left\{ \frac{36}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-x-1)& = & 3 \color{red}{+} (3+4x) \\\Leftrightarrow & -5x-5& = &3+3+4x \\\Leftrightarrow & -5x \color{red}{-5} & = &6 \color{red}{+4x} \\\Leftrightarrow & -5x \color{red}{-5} \color{blue}{+5} \color{blue}{-4x} & = &6 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+5} \\\Leftrightarrow & -5x-4x& = &6+5 \\\Leftrightarrow & -9x& = &11 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{11}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-11}{9} & & \\ & V = \left\{ \frac{-11}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (2x+3)& = & -3 \color{red}{-} (-4+x) \\\Leftrightarrow & 12x+18& = &-3+4-x \\\Leftrightarrow & 12x \color{red}{+18} & = &1 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 12x+x& = &1-18 \\\Leftrightarrow & 13x& = &-17 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-17}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-17}{13} & & \\ & V = \left\{ \frac{-17}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (2x-1)& = & -10 \color{red}{-} (-10-5x) \\\Leftrightarrow & 6x-3& = &-10+10+5x \\\Leftrightarrow & 6x \color{red}{-3} & = &0 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-3} \color{blue}{+3} \color{blue}{-5x} & = &0 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+3} \\\Leftrightarrow & 6x-5x& = &0+3 \\\Leftrightarrow & x& = &3 \\ & V = \left\{ 3 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-2x-3)& = & -14 \color{red}{+} (5+3x) \\\Leftrightarrow & -10x-15& = &-14+5+3x \\\Leftrightarrow & -10x \color{red}{-15} & = &-9 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-15} \color{blue}{+15} \color{blue}{-3x} & = &-9 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+15} \\\Leftrightarrow & -10x-3x& = &-9+15 \\\Leftrightarrow & -13x& = &6 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{6}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-6}{13} & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-5x-5)& = & 4 \color{red}{+} (-8+x) \\\Leftrightarrow & -30x-30& = &4-8+x \\\Leftrightarrow & -30x \color{red}{-30} & = &-4 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & -30x-x& = &-4+30 \\\Leftrightarrow & -31x& = &26 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{26}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-26}{31} & & \\ & V = \left\{ \frac{-26}{31} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (4x+3)& = & 11 \color{red}{-} (8-5x) \\\Leftrightarrow & 16x+12& = &11-8+5x \\\Leftrightarrow & 16x \color{red}{+12} & = &3 \color{red}{+5x} \\\Leftrightarrow & 16x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &3 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & 16x-5x& = &3-12 \\\Leftrightarrow & 11x& = &-9 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-9}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-9}{11} & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (x+5)& = & 10 \color{red}{-} (-10+3x) \\\Leftrightarrow & 4x+20& = &10+10-3x \\\Leftrightarrow & 4x \color{red}{+20} & = &20 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+20} \color{blue}{-20} \color{blue}{+3x} & = &20 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-20} \\\Leftrightarrow & 4x+3x& = &20-20 \\\Leftrightarrow & 7x& = &0 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{0}{ \color{red}{7} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-6x-6)& = & -6 \color{red}{+} (15+x) \\\Leftrightarrow & -30x-30& = &-6+15+x \\\Leftrightarrow & -30x \color{red}{-30} & = &9 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & -30x-x& = &9+30 \\\Leftrightarrow & -31x& = &39 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{39}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-39}{31} & & \\ & V = \left\{ \frac{-39}{31} \right\} & \\\end{align}\)