Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (2x-6)& = & -8 \color{red}{+} (-14+x) \\\Leftrightarrow & 10x-30& = &-8-14+x \\\Leftrightarrow & 10x \color{red}{-30} & = &-22 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &-22 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 10x-x& = &-22+30 \\\Leftrightarrow & 9x& = &8 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{8}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{8}{9} & & \\ & V = \left\{ \frac{8}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-x+3)& = & 13 \color{red}{+} (4+x) \\\Leftrightarrow & -2x+6& = &13+4+x \\\Leftrightarrow & -2x \color{red}{+6} & = &17 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &17 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -2x-x& = &17-6 \\\Leftrightarrow & -3x& = &11 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{11}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-11}{3} & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (3x-2)& = & -6 \color{red}{-} (-2-5x) \\\Leftrightarrow & 6x-4& = &-6+2+5x \\\Leftrightarrow & 6x \color{red}{-4} & = &-4 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-4} \color{blue}{+4} \color{blue}{-5x} & = &-4 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+4} \\\Leftrightarrow & 6x-5x& = &-4+4 \\\Leftrightarrow & x& = &0 \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (5x-3)& = & -2 \color{red}{+} (14+x) \\\Leftrightarrow & 30x-18& = &-2+14+x \\\Leftrightarrow & 30x \color{red}{-18} & = &12 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & 30x-x& = &12+18 \\\Leftrightarrow & 29x& = &30 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{30}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{30}{29} & & \\ & V = \left\{ \frac{30}{29} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (6x+6)& = & 15 \color{red}{-} (11-5x) \\\Leftrightarrow & 18x+18& = &15-11+5x \\\Leftrightarrow & 18x \color{red}{+18} & = &4 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{+18} \color{blue}{-18} \color{blue}{-5x} & = &4 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-18} \\\Leftrightarrow & 18x-5x& = &4-18 \\\Leftrightarrow & 13x& = &-14 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-14}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-14}{13} & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-x+6)& = & 14 \color{red}{-} (6+x) \\\Leftrightarrow & -6x+36& = &14-6-x \\\Leftrightarrow & -6x \color{red}{+36} & = &8 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & -6x+x& = &8-36 \\\Leftrightarrow & -5x& = &-28 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-28}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{28}{5} & & \\ & V = \left\{ \frac{28}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-x+3)& = & -6 \color{red}{+} (7+2x) \\\Leftrightarrow & -3x+9& = &-6+7+2x \\\Leftrightarrow & -3x \color{red}{+9} & = &1 \color{red}{+2x} \\\Leftrightarrow & -3x \color{red}{+9} \color{blue}{-9} \color{blue}{-2x} & = &1 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-9} \\\Leftrightarrow & -3x-2x& = &1-9 \\\Leftrightarrow & -5x& = &-8 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-8}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{8}{5} & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (3x+6)& = & -3 \color{red}{-} (-11+x) \\\Leftrightarrow & 9x+18& = &-3+11-x \\\Leftrightarrow & 9x \color{red}{+18} & = &8 \color{red}{-x} \\\Leftrightarrow & 9x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 9x+x& = &8-18 \\\Leftrightarrow & 10x& = &-10 \\\Leftrightarrow & \frac{10x}{ \color{red}{10} }& = &\frac{-10}{ \color{red}{10} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (2x-2)& = & 10 \color{red}{-} (13+3x) \\\Leftrightarrow & 8x-8& = &10-13-3x \\\Leftrightarrow & 8x \color{red}{-8} & = &-3 \color{red}{-3x} \\\Leftrightarrow & 8x \color{red}{-8} \color{blue}{+8} \color{blue}{+3x} & = &-3 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+8} \\\Leftrightarrow & 8x+3x& = &-3+8 \\\Leftrightarrow & 11x& = &5 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{5}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{5}{11} & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-6x+6)& = & 11 \color{red}{-} (5-5x) \\\Leftrightarrow & -18x+18& = &11-5+5x \\\Leftrightarrow & -18x \color{red}{+18} & = &6 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{+18} \color{blue}{-18} \color{blue}{-5x} & = &6 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-18} \\\Leftrightarrow & -18x-5x& = &6-18 \\\Leftrightarrow & -23x& = &-12 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-12}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{12}{23} & & \\ & V = \left\{ \frac{12}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (4x-6)& = & 6 \color{red}{-} (-13+3x) \\\Leftrightarrow & 20x-30& = &6+13-3x \\\Leftrightarrow & 20x \color{red}{-30} & = &19 \color{red}{-3x} \\\Leftrightarrow & 20x \color{red}{-30} \color{blue}{+30} \color{blue}{+3x} & = &19 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+30} \\\Leftrightarrow & 20x+3x& = &19+30 \\\Leftrightarrow & 23x& = &49 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{49}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{49}{23} & & \\ & V = \left\{ \frac{49}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-4x-3)& = & -6 \color{red}{+} (15+x) \\\Leftrightarrow & -16x-12& = &-6+15+x \\\Leftrightarrow & -16x \color{red}{-12} & = &9 \color{red}{+x} \\\Leftrightarrow & -16x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -16x-x& = &9+12 \\\Leftrightarrow & -17x& = &21 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{21}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-21}{17} & & \\ & V = \left\{ \frac{-21}{17} \right\} & \\\end{align}\)