Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-x-5)& = & 6 \color{red}{-} (2+3x) \\\Leftrightarrow & -2x-10& = &6-2-3x \\\Leftrightarrow & -2x \color{red}{-10} & = &4 \color{red}{-3x} \\\Leftrightarrow & -2x \color{red}{-10} \color{blue}{+10} \color{blue}{+3x} & = &4 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+10} \\\Leftrightarrow & -2x+3x& = &4+10 \\\Leftrightarrow & x& = &14 \\ & V = \left\{ 14 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-3x+1)& = & 12 \color{red}{-} (-2-2x) \\\Leftrightarrow & -15x+5& = &12+2+2x \\\Leftrightarrow & -15x \color{red}{+5} & = &14 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+5} \color{blue}{-5} \color{blue}{-2x} & = &14 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-5} \\\Leftrightarrow & -15x-2x& = &14-5 \\\Leftrightarrow & -17x& = &9 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{9}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-9}{17} & & \\ & V = \left\{ \frac{-9}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-6x-6)& = & -6 \color{red}{-} (-5+x) \\\Leftrightarrow & -12x-12& = &-6+5-x \\\Leftrightarrow & -12x \color{red}{-12} & = &-1 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -12x+x& = &-1+12 \\\Leftrightarrow & -11x& = &11 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{11}{ \color{red}{-11} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-4x+7)& = & -13 \color{red}{-} (4+x) \\\Leftrightarrow & -24x+42& = &-13-4-x \\\Leftrightarrow & -24x \color{red}{+42} & = &-17 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & -24x+x& = &-17-42 \\\Leftrightarrow & -23x& = &-59 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-59}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{59}{23} & & \\ & V = \left\{ \frac{59}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (x-2)& = & -14 \color{red}{+} (14+x) \\\Leftrightarrow & 6x-12& = &-14+14+x \\\Leftrightarrow & 6x \color{red}{-12} & = &0 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 6x-x& = &0+12 \\\Leftrightarrow & 5x& = &12 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{12}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{12}{5} & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-x+5)& = & 4 \color{red}{-} (-10+2x) \\\Leftrightarrow & -5x+25& = &4+10-2x \\\Leftrightarrow & -5x \color{red}{+25} & = &14 \color{red}{-2x} \\\Leftrightarrow & -5x \color{red}{+25} \color{blue}{-25} \color{blue}{+2x} & = &14 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-25} \\\Leftrightarrow & -5x+2x& = &14-25 \\\Leftrightarrow & -3x& = &-11 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-11}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{11}{3} & & \\ & V = \left\{ \frac{11}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-6x-3)& = & -5 \color{red}{+} (-14+x) \\\Leftrightarrow & -24x-12& = &-5-14+x \\\Leftrightarrow & -24x \color{red}{-12} & = &-19 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -24x-x& = &-19+12 \\\Leftrightarrow & -25x& = &-7 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-7}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{7}{25} & & \\ & V = \left\{ \frac{7}{25} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (3x+2)& = & -14 \color{red}{+} (-6+2x) \\\Leftrightarrow & 15x+10& = &-14-6+2x \\\Leftrightarrow & 15x \color{red}{+10} & = &-20 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+10} \color{blue}{-10} \color{blue}{-2x} & = &-20 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-10} \\\Leftrightarrow & 15x-2x& = &-20-10 \\\Leftrightarrow & 13x& = &-30 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-30}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-30}{13} & & \\ & V = \left\{ \frac{-30}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-2x-3)& = & -4 \color{red}{+} (-8+x) \\\Leftrightarrow & -10x-15& = &-4-8+x \\\Leftrightarrow & -10x \color{red}{-15} & = &-12 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & -10x-x& = &-12+15 \\\Leftrightarrow & -11x& = &3 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{3}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-3}{11} & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (x+4)& = & 2 \color{red}{-} (2-2x) \\\Leftrightarrow & 5x+20& = &2-2+2x \\\Leftrightarrow & 5x \color{red}{+20} & = &0 \color{red}{+2x} \\\Leftrightarrow & 5x \color{red}{+20} \color{blue}{-20} \color{blue}{-2x} & = &0 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-20} \\\Leftrightarrow & 5x-2x& = &0-20 \\\Leftrightarrow & 3x& = &-20 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-20}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-20}{3} & & \\ & V = \left\{ \frac{-20}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-5x-2)& = & 7 \color{red}{-} (-9+x) \\\Leftrightarrow & -30x-12& = &7+9-x \\\Leftrightarrow & -30x \color{red}{-12} & = &16 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -30x+x& = &16+12 \\\Leftrightarrow & -29x& = &28 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{28}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-28}{29} & & \\ & V = \left\{ \frac{-28}{29} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-x-6)& = & 13 \color{red}{-} (14+x) \\\Leftrightarrow & -6x-36& = &13-14-x \\\Leftrightarrow & -6x \color{red}{-36} & = &-1 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & -6x+x& = &-1+36 \\\Leftrightarrow & -5x& = &35 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{35}{ \color{red}{-5} } \\\Leftrightarrow & x = -7 & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)