Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (2x+4)& = & -13 \color{red}{+} (-10+x) \\\Leftrightarrow & 12x+24& = &-13-10+x \\\Leftrightarrow & 12x \color{red}{+24} & = &-23 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-23 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 12x-x& = &-23-24 \\\Leftrightarrow & 11x& = &-47 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-47}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-47}{11} & & \\ & V = \left\{ \frac{-47}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-4x+2)& = & -11 \color{red}{-} (12+x) \\\Leftrightarrow & -12x+6& = &-11-12-x \\\Leftrightarrow & -12x \color{red}{+6} & = &-23 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-23 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -12x+x& = &-23-6 \\\Leftrightarrow & -11x& = &-29 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-29}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{29}{11} & & \\ & V = \left\{ \frac{29}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-3x-5)& = & 3 \color{red}{+} (11-5x) \\\Leftrightarrow & -18x-30& = &3+11-5x \\\Leftrightarrow & -18x \color{red}{-30} & = &14 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-30} \color{blue}{+30} \color{blue}{+5x} & = &14 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+30} \\\Leftrightarrow & -18x+5x& = &14+30 \\\Leftrightarrow & -13x& = &44 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{44}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-44}{13} & & \\ & V = \left\{ \frac{-44}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-2x+6)& = & 6 \color{red}{+} (3-3x) \\\Leftrightarrow & -10x+30& = &6+3-3x \\\Leftrightarrow & -10x \color{red}{+30} & = &9 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{+30} \color{blue}{-30} \color{blue}{+3x} & = &9 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-30} \\\Leftrightarrow & -10x+3x& = &9-30 \\\Leftrightarrow & -7x& = &-21 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-21}{ \color{red}{-7} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-x+2)& = & 14 \color{red}{+} (4-2x) \\\Leftrightarrow & -5x+10& = &14+4-2x \\\Leftrightarrow & -5x \color{red}{+10} & = &18 \color{red}{-2x} \\\Leftrightarrow & -5x \color{red}{+10} \color{blue}{-10} \color{blue}{+2x} & = &18 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-10} \\\Leftrightarrow & -5x+2x& = &18-10 \\\Leftrightarrow & -3x& = &8 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{8}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-8}{3} & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-6x+3)& = & 8 \color{red}{+} (-4+x) \\\Leftrightarrow & -12x+6& = &8-4+x \\\Leftrightarrow & -12x \color{red}{+6} & = &4 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -12x-x& = &4-6 \\\Leftrightarrow & -13x& = &-2 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-2}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{2}{13} & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (6x+3)& = & -5 \color{red}{+} (-8+x) \\\Leftrightarrow & 12x+6& = &-5-8+x \\\Leftrightarrow & 12x \color{red}{+6} & = &-13 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 12x-x& = &-13-6 \\\Leftrightarrow & 11x& = &-19 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-19}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-19}{11} & & \\ & V = \left\{ \frac{-19}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-5x-1)& = & 5 \color{red}{+} (-6+x) \\\Leftrightarrow & -15x-3& = &5-6+x \\\Leftrightarrow & -15x \color{red}{-3} & = &-1 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{-3} \color{blue}{+3} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{+3} \\\Leftrightarrow & -15x-x& = &-1+3 \\\Leftrightarrow & -16x& = &2 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{2}{ \color{red}{-16} } \\\Leftrightarrow & x = \frac{-1}{8} & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-2x-2)& = & 4 \color{red}{-} (-14+3x) \\\Leftrightarrow & -4x-4& = &4+14-3x \\\Leftrightarrow & -4x \color{red}{-4} & = &18 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-4} \color{blue}{+4} \color{blue}{+3x} & = &18 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+4} \\\Leftrightarrow & -4x+3x& = &18+4 \\\Leftrightarrow & -x& = &22 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{22}{ \color{red}{-1} } \\\Leftrightarrow & x = -22 & & \\ & V = \left\{ -22 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-6x+5)& = & 5 \color{red}{-} (-4+x) \\\Leftrightarrow & -24x+20& = &5+4-x \\\Leftrightarrow & -24x \color{red}{+20} & = &9 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & -24x+x& = &9-20 \\\Leftrightarrow & -23x& = &-11 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-11}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{11}{23} & & \\ & V = \left\{ \frac{11}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-3x-2)& = & 9 \color{red}{+} (-2-2x) \\\Leftrightarrow & -15x-10& = &9-2-2x \\\Leftrightarrow & -15x \color{red}{-10} & = &7 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{-10} \color{blue}{+10} \color{blue}{+2x} & = &7 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+10} \\\Leftrightarrow & -15x+2x& = &7+10 \\\Leftrightarrow & -13x& = &17 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{17}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-17}{13} & & \\ & V = \left\{ \frac{-17}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (3x+7)& = & 3 \color{red}{+} (-4+x) \\\Leftrightarrow & 9x+21& = &3-4+x \\\Leftrightarrow & 9x \color{red}{+21} & = &-1 \color{red}{+x} \\\Leftrightarrow & 9x \color{red}{+21} \color{blue}{-21} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-21} \\\Leftrightarrow & 9x-x& = &-1-21 \\\Leftrightarrow & 8x& = &-22 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{-22}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{-11}{4} & & \\ & V = \left\{ \frac{-11}{4} \right\} & \\\end{align}\)