Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (5x+5)& = & -10 \color{red}{+} (15-3x) \\\Leftrightarrow & 10x+10& = &-10+15-3x \\\Leftrightarrow & 10x \color{red}{+10} & = &5 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+10} \color{blue}{-10} \color{blue}{+3x} & = &5 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-10} \\\Leftrightarrow & 10x+3x& = &5-10 \\\Leftrightarrow & 13x& = &-5 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-5}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-5}{13} & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-x+3)& = & -14 \color{red}{-} (-10+x) \\\Leftrightarrow & -4x+12& = &-14+10-x \\\Leftrightarrow & -4x \color{red}{+12} & = &-4 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -4x+x& = &-4-12 \\\Leftrightarrow & -3x& = &-16 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-16}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{16}{3} & & \\ & V = \left\{ \frac{16}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-3x+3)& = & 10 \color{red}{-} (10+x) \\\Leftrightarrow & -12x+12& = &10-10-x \\\Leftrightarrow & -12x \color{red}{+12} & = &0 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -12x+x& = &0-12 \\\Leftrightarrow & -11x& = &-12 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-12}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{12}{11} & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-x-6)& = & 3 \color{red}{-} (5+x) \\\Leftrightarrow & -6x-36& = &3-5-x \\\Leftrightarrow & -6x \color{red}{-36} & = &-2 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & -6x+x& = &-2+36 \\\Leftrightarrow & -5x& = &34 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{34}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-34}{5} & & \\ & V = \left\{ \frac{-34}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (6x-2)& = & -3 \color{red}{-} (1+x) \\\Leftrightarrow & 36x-12& = &-3-1-x \\\Leftrightarrow & 36x \color{red}{-12} & = &-4 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 36x+x& = &-4+12 \\\Leftrightarrow & 37x& = &8 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{8}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{8}{37} & & \\ & V = \left\{ \frac{8}{37} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-5x+3)& = & 6 \color{red}{-} (-9-2x) \\\Leftrightarrow & -15x+9& = &6+9+2x \\\Leftrightarrow & -15x \color{red}{+9} & = &15 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+9} \color{blue}{-9} \color{blue}{-2x} & = &15 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-9} \\\Leftrightarrow & -15x-2x& = &15-9 \\\Leftrightarrow & -17x& = &6 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{6}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-6}{17} & & \\ & V = \left\{ \frac{-6}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (x+2)& = & -2 \color{red}{+} (-2+2x) \\\Leftrightarrow & 5x+10& = &-2-2+2x \\\Leftrightarrow & 5x \color{red}{+10} & = &-4 \color{red}{+2x} \\\Leftrightarrow & 5x \color{red}{+10} \color{blue}{-10} \color{blue}{-2x} & = &-4 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-10} \\\Leftrightarrow & 5x-2x& = &-4-10 \\\Leftrightarrow & 3x& = &-14 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-14}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-14}{3} & & \\ & V = \left\{ \frac{-14}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (6x-1)& = & 1 \color{red}{+} (13+x) \\\Leftrightarrow & 24x-4& = &1+13+x \\\Leftrightarrow & 24x \color{red}{-4} & = &14 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & 24x-x& = &14+4 \\\Leftrightarrow & 23x& = &18 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{18}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{18}{23} & & \\ & V = \left\{ \frac{18}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-6x-3)& = & -6 \color{red}{+} (-14+x) \\\Leftrightarrow & -36x-18& = &-6-14+x \\\Leftrightarrow & -36x \color{red}{-18} & = &-20 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-20 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & -36x-x& = &-20+18 \\\Leftrightarrow & -37x& = &-2 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{-2}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{2}{37} & & \\ & V = \left\{ \frac{2}{37} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (2x-7)& = & -11 \color{red}{+} (-2-5x) \\\Leftrightarrow & 6x-21& = &-11-2-5x \\\Leftrightarrow & 6x \color{red}{-21} & = &-13 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-21} \color{blue}{+21} \color{blue}{+5x} & = &-13 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+21} \\\Leftrightarrow & 6x+5x& = &-13+21 \\\Leftrightarrow & 11x& = &8 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{8}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{8}{11} & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (5x-7)& = & 12 \color{red}{-} (-7-3x) \\\Leftrightarrow & 10x-14& = &12+7+3x \\\Leftrightarrow & 10x \color{red}{-14} & = &19 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-14} \color{blue}{+14} \color{blue}{-3x} & = &19 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+14} \\\Leftrightarrow & 10x-3x& = &19+14 \\\Leftrightarrow & 7x& = &33 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{33}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{33}{7} & & \\ & V = \left\{ \frac{33}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-5x+3)& = & -2 \color{red}{+} (-11-3x) \\\Leftrightarrow & -10x+6& = &-2-11-3x \\\Leftrightarrow & -10x \color{red}{+6} & = &-13 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{+6} \color{blue}{-6} \color{blue}{+3x} & = &-13 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-6} \\\Leftrightarrow & -10x+3x& = &-13-6 \\\Leftrightarrow & -7x& = &-19 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-19}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{19}{7} & & \\ & V = \left\{ \frac{19}{7} \right\} & \\\end{align}\)