Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (4x-3)& = & -8 \color{red}{+} (-2+x) \\\Leftrightarrow & 24x-18& = &-8-2+x \\\Leftrightarrow & 24x \color{red}{-18} & = &-10 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & 24x-x& = &-10+18 \\\Leftrightarrow & 23x& = &8 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{8}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{8}{23} & & \\ & V = \left\{ \frac{8}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (4x-1)& = & -15 \color{red}{-} (-5+x) \\\Leftrightarrow & 20x-5& = &-15+5-x \\\Leftrightarrow & 20x \color{red}{-5} & = &-10 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-5} \color{blue}{+5} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{+5} \\\Leftrightarrow & 20x+x& = &-10+5 \\\Leftrightarrow & 21x& = &-5 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-5}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-5}{21} & & \\ & V = \left\{ \frac{-5}{21} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (x-5)& = & -13 \color{red}{+} (-14+2x) \\\Leftrightarrow & 3x-15& = &-13-14+2x \\\Leftrightarrow & 3x \color{red}{-15} & = &-27 \color{red}{+2x} \\\Leftrightarrow & 3x \color{red}{-15} \color{blue}{+15} \color{blue}{-2x} & = &-27 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+15} \\\Leftrightarrow & 3x-2x& = &-27+15 \\\Leftrightarrow & x& = &-12 \\ & V = \left\{ -12 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (2x+6)& = & 14 \color{red}{+} (6-5x) \\\Leftrightarrow & 6x+18& = &14+6-5x \\\Leftrightarrow & 6x \color{red}{+18} & = &20 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+18} \color{blue}{-18} \color{blue}{+5x} & = &20 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-18} \\\Leftrightarrow & 6x+5x& = &20-18 \\\Leftrightarrow & 11x& = &2 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{2}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{2}{11} & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (x+1)& = & -5 \color{red}{+} (12-2x) \\\Leftrightarrow & 3x+3& = &-5+12-2x \\\Leftrightarrow & 3x \color{red}{+3} & = &7 \color{red}{-2x} \\\Leftrightarrow & 3x \color{red}{+3} \color{blue}{-3} \color{blue}{+2x} & = &7 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-3} \\\Leftrightarrow & 3x+2x& = &7-3 \\\Leftrightarrow & 5x& = &4 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{4}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{4}{5} & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-5x+7)& = & -1 \color{red}{-} (-6+x) \\\Leftrightarrow & -20x+28& = &-1+6-x \\\Leftrightarrow & -20x \color{red}{+28} & = &5 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & -20x+x& = &5-28 \\\Leftrightarrow & -19x& = &-23 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-23}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{23}{19} & & \\ & V = \left\{ \frac{23}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (4x-2)& = & 1 \color{red}{+} (-11+x) \\\Leftrightarrow & 8x-4& = &1-11+x \\\Leftrightarrow & 8x \color{red}{-4} & = &-10 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & 8x-x& = &-10+4 \\\Leftrightarrow & 7x& = &-6 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-6}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-6}{7} & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-3x-5)& = & -7 \color{red}{-} (-13-4x) \\\Leftrightarrow & -9x-15& = &-7+13+4x \\\Leftrightarrow & -9x \color{red}{-15} & = &6 \color{red}{+4x} \\\Leftrightarrow & -9x \color{red}{-15} \color{blue}{+15} \color{blue}{-4x} & = &6 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+15} \\\Leftrightarrow & -9x-4x& = &6+15 \\\Leftrightarrow & -13x& = &21 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{21}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-21}{13} & & \\ & V = \left\{ \frac{-21}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (4x+2)& = & -6 \color{red}{-} (9-5x) \\\Leftrightarrow & 16x+8& = &-6-9+5x \\\Leftrightarrow & 16x \color{red}{+8} & = &-15 \color{red}{+5x} \\\Leftrightarrow & 16x \color{red}{+8} \color{blue}{-8} \color{blue}{-5x} & = &-15 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-8} \\\Leftrightarrow & 16x-5x& = &-15-8 \\\Leftrightarrow & 11x& = &-23 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-23}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-23}{11} & & \\ & V = \left\{ \frac{-23}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (x+3)& = & 13 \color{red}{-} (-15-5x) \\\Leftrightarrow & 6x+18& = &13+15+5x \\\Leftrightarrow & 6x \color{red}{+18} & = &28 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+18} \color{blue}{-18} \color{blue}{-5x} & = &28 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-18} \\\Leftrightarrow & 6x-5x& = &28-18 \\\Leftrightarrow & x& = &10 \\ & V = \left\{ 10 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (3x-3)& = & -8 \color{red}{-} (14-5x) \\\Leftrightarrow & 6x-6& = &-8-14+5x \\\Leftrightarrow & 6x \color{red}{-6} & = &-22 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-6} \color{blue}{+6} \color{blue}{-5x} & = &-22 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+6} \\\Leftrightarrow & 6x-5x& = &-22+6 \\\Leftrightarrow & x& = &-16 \\ & V = \left\{ -16 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (3x+4)& = & 10 \color{red}{+} (8+x) \\\Leftrightarrow & 12x+16& = &10+8+x \\\Leftrightarrow & 12x \color{red}{+16} & = &18 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &18 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & 12x-x& = &18-16 \\\Leftrightarrow & 11x& = &2 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{2}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{2}{11} & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)