Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (3x-3)& = & -1 \color{red}{+} (-1-5x) \\\Leftrightarrow & 18x-18& = &-1-1-5x \\\Leftrightarrow & 18x \color{red}{-18} & = &-2 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-18} \color{blue}{+18} \color{blue}{+5x} & = &-2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+18} \\\Leftrightarrow & 18x+5x& = &-2+18 \\\Leftrightarrow & 23x& = &16 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{16}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{16}{23} & & \\ & V = \left\{ \frac{16}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (x-2)& = & -14 \color{red}{-} (13+x) \\\Leftrightarrow & 2x-4& = &-14-13-x \\\Leftrightarrow & 2x \color{red}{-4} & = &-27 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-27 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 2x+x& = &-27+4 \\\Leftrightarrow & 3x& = &-23 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-23}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-23}{3} & & \\ & V = \left\{ \frac{-23}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (6x+6)& = & 14 \color{red}{+} (7+x) \\\Leftrightarrow & 12x+12& = &14+7+x \\\Leftrightarrow & 12x \color{red}{+12} & = &21 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &21 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 12x-x& = &21-12 \\\Leftrightarrow & 11x& = &9 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{9}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{9}{11} & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-5x-5)& = & -12 \color{red}{-} (-3-2x) \\\Leftrightarrow & -15x-15& = &-12+3+2x \\\Leftrightarrow & -15x \color{red}{-15} & = &-9 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{-15} \color{blue}{+15} \color{blue}{-2x} & = &-9 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+15} \\\Leftrightarrow & -15x-2x& = &-9+15 \\\Leftrightarrow & -17x& = &6 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{6}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-6}{17} & & \\ & V = \left\{ \frac{-6}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (x-3)& = & 14 \color{red}{-} (-3+4x) \\\Leftrightarrow & 3x-9& = &14+3-4x \\\Leftrightarrow & 3x \color{red}{-9} & = &17 \color{red}{-4x} \\\Leftrightarrow & 3x \color{red}{-9} \color{blue}{+9} \color{blue}{+4x} & = &17 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+9} \\\Leftrightarrow & 3x+4x& = &17+9 \\\Leftrightarrow & 7x& = &26 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{26}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{26}{7} & & \\ & V = \left\{ \frac{26}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (x-5)& = & -2 \color{red}{-} (10+x) \\\Leftrightarrow & 3x-15& = &-2-10-x \\\Leftrightarrow & 3x \color{red}{-15} & = &-12 \color{red}{-x} \\\Leftrightarrow & 3x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & 3x+x& = &-12+15 \\\Leftrightarrow & 4x& = &3 \\\Leftrightarrow & \frac{4x}{ \color{red}{4} }& = &\frac{3}{ \color{red}{4} } \\\Leftrightarrow & x = \frac{3}{4} & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-4x+5)& = & 2 \color{red}{-} (-10+x) \\\Leftrightarrow & -16x+20& = &2+10-x \\\Leftrightarrow & -16x \color{red}{+20} & = &12 \color{red}{-x} \\\Leftrightarrow & -16x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & -16x+x& = &12-20 \\\Leftrightarrow & -15x& = &-8 \\\Leftrightarrow & \frac{-15x}{ \color{red}{-15} }& = &\frac{-8}{ \color{red}{-15} } \\\Leftrightarrow & x = \frac{8}{15} & & \\ & V = \left\{ \frac{8}{15} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (3x-1)& = & 1 \color{red}{+} (-12+x) \\\Leftrightarrow & 6x-2& = &1-12+x \\\Leftrightarrow & 6x \color{red}{-2} & = &-11 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & 6x-x& = &-11+2 \\\Leftrightarrow & 5x& = &-9 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-9}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-9}{5} & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-6x-6)& = & 7 \color{red}{-} (1+x) \\\Leftrightarrow & -18x-18& = &7-1-x \\\Leftrightarrow & -18x \color{red}{-18} & = &6 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & -18x+x& = &6+18 \\\Leftrightarrow & -17x& = &24 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{24}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-24}{17} & & \\ & V = \left\{ \frac{-24}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (x+6)& = & -4 \color{red}{+} (-10-5x) \\\Leftrightarrow & 6x+36& = &-4-10-5x \\\Leftrightarrow & 6x \color{red}{+36} & = &-14 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+36} \color{blue}{-36} \color{blue}{+5x} & = &-14 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-36} \\\Leftrightarrow & 6x+5x& = &-14-36 \\\Leftrightarrow & 11x& = &-50 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-50}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-50}{11} & & \\ & V = \left\{ \frac{-50}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (5x-5)& = & 10 \color{red}{-} (8+x) \\\Leftrightarrow & 10x-10& = &10-8-x \\\Leftrightarrow & 10x \color{red}{-10} & = &2 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 10x+x& = &2+10 \\\Leftrightarrow & 11x& = &12 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{12}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{12}{11} & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-4x+2)& = & -2 \color{red}{-} (15-5x) \\\Leftrightarrow & -8x+4& = &-2-15+5x \\\Leftrightarrow & -8x \color{red}{+4} & = &-17 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{+4} \color{blue}{-4} \color{blue}{-5x} & = &-17 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-4} \\\Leftrightarrow & -8x-5x& = &-17-4 \\\Leftrightarrow & -13x& = &-21 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-21}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{21}{13} & & \\ & V = \left\{ \frac{21}{13} \right\} & \\\end{align}\)