Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (4x-6)& = & -3 \color{red}{+} (10+x) \\\Leftrightarrow & 20x-30& = &-3+10+x \\\Leftrightarrow & 20x \color{red}{-30} & = &7 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 20x-x& = &7+30 \\\Leftrightarrow & 19x& = &37 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{37}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{37}{19} & & \\ & V = \left\{ \frac{37}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (3x-6)& = & 11 \color{red}{+} (-1+x) \\\Leftrightarrow & 12x-24& = &11-1+x \\\Leftrightarrow & 12x \color{red}{-24} & = &10 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 12x-x& = &10+24 \\\Leftrightarrow & 11x& = &34 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{34}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{34}{11} & & \\ & V = \left\{ \frac{34}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (3x+1)& = & -8 \color{red}{+} (-4-2x) \\\Leftrightarrow & 15x+5& = &-8-4-2x \\\Leftrightarrow & 15x \color{red}{+5} & = &-12 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{+5} \color{blue}{-5} \color{blue}{+2x} & = &-12 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-5} \\\Leftrightarrow & 15x+2x& = &-12-5 \\\Leftrightarrow & 17x& = &-17 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-17}{ \color{red}{17} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-5x+1)& = & -10 \color{red}{-} (-7+x) \\\Leftrightarrow & -15x+3& = &-10+7-x \\\Leftrightarrow & -15x \color{red}{+3} & = &-3 \color{red}{-x} \\\Leftrightarrow & -15x \color{red}{+3} \color{blue}{-3} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{-3} \\\Leftrightarrow & -15x+x& = &-3-3 \\\Leftrightarrow & -14x& = &-6 \\\Leftrightarrow & \frac{-14x}{ \color{red}{-14} }& = &\frac{-6}{ \color{red}{-14} } \\\Leftrightarrow & x = \frac{3}{7} & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (x+7)& = & 2 \color{red}{-} (6+4x) \\\Leftrightarrow & 5x+35& = &2-6-4x \\\Leftrightarrow & 5x \color{red}{+35} & = &-4 \color{red}{-4x} \\\Leftrightarrow & 5x \color{red}{+35} \color{blue}{-35} \color{blue}{+4x} & = &-4 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-35} \\\Leftrightarrow & 5x+4x& = &-4-35 \\\Leftrightarrow & 9x& = &-39 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-39}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-13}{3} & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-6x-5)& = & 14 \color{red}{+} (-4+x) \\\Leftrightarrow & -30x-25& = &14-4+x \\\Leftrightarrow & -30x \color{red}{-25} & = &10 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-25} \color{blue}{+25} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{+25} \\\Leftrightarrow & -30x-x& = &10+25 \\\Leftrightarrow & -31x& = &35 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{35}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-35}{31} & & \\ & V = \left\{ \frac{-35}{31} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (5x-3)& = & -13 \color{red}{+} (-5+x) \\\Leftrightarrow & 30x-18& = &-13-5+x \\\Leftrightarrow & 30x \color{red}{-18} & = &-18 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-18 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & 30x-x& = &-18+18 \\\Leftrightarrow & 29x& = &0 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{0}{ \color{red}{29} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-3x+3)& = & 13 \color{red}{-} (-15+2x) \\\Leftrightarrow & -15x+15& = &13+15-2x \\\Leftrightarrow & -15x \color{red}{+15} & = &28 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+15} \color{blue}{-15} \color{blue}{+2x} & = &28 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-15} \\\Leftrightarrow & -15x+2x& = &28-15 \\\Leftrightarrow & -13x& = &13 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{13}{ \color{red}{-13} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-6x-1)& = & 14 \color{red}{-} (-13+x) \\\Leftrightarrow & -18x-3& = &14+13-x \\\Leftrightarrow & -18x \color{red}{-3} & = &27 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-3} \color{blue}{+3} \color{blue}{+x} & = &27 \color{red}{-x} \color{blue}{+x} \color{blue}{+3} \\\Leftrightarrow & -18x+x& = &27+3 \\\Leftrightarrow & -17x& = &30 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{30}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-30}{17} & & \\ & V = \left\{ \frac{-30}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-6x-6)& = & -14 \color{red}{-} (10+x) \\\Leftrightarrow & -24x-24& = &-14-10-x \\\Leftrightarrow & -24x \color{red}{-24} & = &-24 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-24 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -24x+x& = &-24+24 \\\Leftrightarrow & -23x& = &0 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{0}{ \color{red}{-23} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-6x+2)& = & -15 \color{red}{+} (1+x) \\\Leftrightarrow & -30x+10& = &-15+1+x \\\Leftrightarrow & -30x \color{red}{+10} & = &-14 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & -30x-x& = &-14-10 \\\Leftrightarrow & -31x& = &-24 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-24}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{24}{31} & & \\ & V = \left\{ \frac{24}{31} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (2x+2)& = & 3 \color{red}{+} (10+x) \\\Leftrightarrow & 12x+12& = &3+10+x \\\Leftrightarrow & 12x \color{red}{+12} & = &13 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 12x-x& = &13-12 \\\Leftrightarrow & 11x& = &1 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{1}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{1}{11} & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)