Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-5x-1)& = & -2 \color{red}{-} (8+x) \\\Leftrightarrow & -20x-4& = &-2-8-x \\\Leftrightarrow & -20x \color{red}{-4} & = &-10 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & -20x+x& = &-10+4 \\\Leftrightarrow & -19x& = &-6 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-6}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{6}{19} & & \\ & V = \left\{ \frac{6}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-6x-4)& = & 8 \color{red}{-} (-14+x) \\\Leftrightarrow & -24x-16& = &8+14-x \\\Leftrightarrow & -24x \color{red}{-16} & = &22 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &22 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & -24x+x& = &22+16 \\\Leftrightarrow & -23x& = &38 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{38}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-38}{23} & & \\ & V = \left\{ \frac{-38}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (3x+3)& = & -8 \color{red}{+} (4+x) \\\Leftrightarrow & 12x+12& = &-8+4+x \\\Leftrightarrow & 12x \color{red}{+12} & = &-4 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 12x-x& = &-4-12 \\\Leftrightarrow & 11x& = &-16 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-16}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-16}{11} & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-6x+2)& = & -9 \color{red}{+} (-3-5x) \\\Leftrightarrow & -36x+12& = &-9-3-5x \\\Leftrightarrow & -36x \color{red}{+12} & = &-12 \color{red}{-5x} \\\Leftrightarrow & -36x \color{red}{+12} \color{blue}{-12} \color{blue}{+5x} & = &-12 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-12} \\\Leftrightarrow & -36x+5x& = &-12-12 \\\Leftrightarrow & -31x& = &-24 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-24}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{24}{31} & & \\ & V = \left\{ \frac{24}{31} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-6x+5)& = & 13 \color{red}{+} (5+x) \\\Leftrightarrow & -18x+15& = &13+5+x \\\Leftrightarrow & -18x \color{red}{+15} & = &18 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &18 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & -18x-x& = &18-15 \\\Leftrightarrow & -19x& = &3 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{3}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-3}{19} & & \\ & V = \left\{ \frac{-3}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-3x+3)& = & -3 \color{red}{-} (1-5x) \\\Leftrightarrow & -18x+18& = &-3-1+5x \\\Leftrightarrow & -18x \color{red}{+18} & = &-4 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{+18} \color{blue}{-18} \color{blue}{-5x} & = &-4 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-18} \\\Leftrightarrow & -18x-5x& = &-4-18 \\\Leftrightarrow & -23x& = &-22 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-22}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{22}{23} & & \\ & V = \left\{ \frac{22}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-6x-7)& = & 6 \color{red}{+} (6+x) \\\Leftrightarrow & -18x-21& = &6+6+x \\\Leftrightarrow & -18x \color{red}{-21} & = &12 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-21} \color{blue}{+21} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{+21} \\\Leftrightarrow & -18x-x& = &12+21 \\\Leftrightarrow & -19x& = &33 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{33}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-33}{19} & & \\ & V = \left\{ \frac{-33}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-5x+7)& = & 5 \color{red}{-} (-11+x) \\\Leftrightarrow & -10x+14& = &5+11-x \\\Leftrightarrow & -10x \color{red}{+14} & = &16 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{+14} \color{blue}{-14} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{-14} \\\Leftrightarrow & -10x+x& = &16-14 \\\Leftrightarrow & -9x& = &2 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{2}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-2}{9} & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (3x+7)& = & -9 \color{red}{+} (14+x) \\\Leftrightarrow & 12x+28& = &-9+14+x \\\Leftrightarrow & 12x \color{red}{+28} & = &5 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & 12x-x& = &5-28 \\\Leftrightarrow & 11x& = &-23 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-23}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-23}{11} & & \\ & V = \left\{ \frac{-23}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-5x-4)& = & -8 \color{red}{-} (8+x) \\\Leftrightarrow & -20x-16& = &-8-8-x \\\Leftrightarrow & -20x \color{red}{-16} & = &-16 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &-16 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & -20x+x& = &-16+16 \\\Leftrightarrow & -19x& = &0 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{0}{ \color{red}{-19} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-x-6)& = & 5 \color{red}{-} (1+2x) \\\Leftrightarrow & -3x-18& = &5-1-2x \\\Leftrightarrow & -3x \color{red}{-18} & = &4 \color{red}{-2x} \\\Leftrightarrow & -3x \color{red}{-18} \color{blue}{+18} \color{blue}{+2x} & = &4 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+18} \\\Leftrightarrow & -3x+2x& = &4+18 \\\Leftrightarrow & -x& = &22 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{22}{ \color{red}{-1} } \\\Leftrightarrow & x = -22 & & \\ & V = \left\{ -22 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-6x+4)& = & -5 \color{red}{+} (11+x) \\\Leftrightarrow & -12x+8& = &-5+11+x \\\Leftrightarrow & -12x \color{red}{+8} & = &6 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -12x-x& = &6-8 \\\Leftrightarrow & -13x& = &-2 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-2}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{2}{13} & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)