Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-2x+2)& = & 1 \color{red}{-} (4+3x) \\\Leftrightarrow & -4x+4& = &1-4-3x \\\Leftrightarrow & -4x \color{red}{+4} & = &-3 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+4} \color{blue}{-4} \color{blue}{+3x} & = &-3 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-4} \\\Leftrightarrow & -4x+3x& = &-3-4 \\\Leftrightarrow & -x& = &-7 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-7}{ \color{red}{-1} } \\\Leftrightarrow & x = 7 & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-2x-5)& = & 15 \color{red}{+} (7-5x) \\\Leftrightarrow & -6x-15& = &15+7-5x \\\Leftrightarrow & -6x \color{red}{-15} & = &22 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-15} \color{blue}{+15} \color{blue}{+5x} & = &22 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+15} \\\Leftrightarrow & -6x+5x& = &22+15 \\\Leftrightarrow & -x& = &37 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{37}{ \color{red}{-1} } \\\Leftrightarrow & x = -37 & & \\ & V = \left\{ -37 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (4x-4)& = & -3 \color{red}{-} (-2+x) \\\Leftrightarrow & 8x-8& = &-3+2-x \\\Leftrightarrow & 8x \color{red}{-8} & = &-1 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 8x+x& = &-1+8 \\\Leftrightarrow & 9x& = &7 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{7}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{7}{9} & & \\ & V = \left\{ \frac{7}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-5x+2)& = & -2 \color{red}{+} (2+4x) \\\Leftrightarrow & -25x+10& = &-2+2+4x \\\Leftrightarrow & -25x \color{red}{+10} & = &0 \color{red}{+4x} \\\Leftrightarrow & -25x \color{red}{+10} \color{blue}{-10} \color{blue}{-4x} & = &0 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-10} \\\Leftrightarrow & -25x-4x& = &0-10 \\\Leftrightarrow & -29x& = &-10 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-10}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{10}{29} & & \\ & V = \left\{ \frac{10}{29} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-x-6)& = & 10 \color{red}{+} (-14+4x) \\\Leftrightarrow & -3x-18& = &10-14+4x \\\Leftrightarrow & -3x \color{red}{-18} & = &-4 \color{red}{+4x} \\\Leftrightarrow & -3x \color{red}{-18} \color{blue}{+18} \color{blue}{-4x} & = &-4 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+18} \\\Leftrightarrow & -3x-4x& = &-4+18 \\\Leftrightarrow & -7x& = &14 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{14}{ \color{red}{-7} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (6x-6)& = & 3 \color{red}{+} (-8+x) \\\Leftrightarrow & 12x-12& = &3-8+x \\\Leftrightarrow & 12x \color{red}{-12} & = &-5 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 12x-x& = &-5+12 \\\Leftrightarrow & 11x& = &7 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{7}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{7}{11} & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (4x-2)& = & 4 \color{red}{+} (-2-5x) \\\Leftrightarrow & 8x-4& = &4-2-5x \\\Leftrightarrow & 8x \color{red}{-4} & = &2 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{-4} \color{blue}{+4} \color{blue}{+5x} & = &2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+4} \\\Leftrightarrow & 8x+5x& = &2+4 \\\Leftrightarrow & 13x& = &6 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{6}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{6}{13} & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-4x+1)& = & 4 \color{red}{-} (-4+3x) \\\Leftrightarrow & -8x+2& = &4+4-3x \\\Leftrightarrow & -8x \color{red}{+2} & = &8 \color{red}{-3x} \\\Leftrightarrow & -8x \color{red}{+2} \color{blue}{-2} \color{blue}{+3x} & = &8 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-2} \\\Leftrightarrow & -8x+3x& = &8-2 \\\Leftrightarrow & -5x& = &6 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{6}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-6}{5} & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (3x-6)& = & 2 \color{red}{-} (-13-5x) \\\Leftrightarrow & 6x-12& = &2+13+5x \\\Leftrightarrow & 6x \color{red}{-12} & = &15 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &15 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & 6x-5x& = &15+12 \\\Leftrightarrow & x& = &27 \\ & V = \left\{ 27 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-5x+5)& = & 2 \color{red}{-} (-3+3x) \\\Leftrightarrow & -10x+10& = &2+3-3x \\\Leftrightarrow & -10x \color{red}{+10} & = &5 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{+10} \color{blue}{-10} \color{blue}{+3x} & = &5 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-10} \\\Leftrightarrow & -10x+3x& = &5-10 \\\Leftrightarrow & -7x& = &-5 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-5}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{5}{7} & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (3x-2)& = & 10 \color{red}{+} (7-2x) \\\Leftrightarrow & 15x-10& = &10+7-2x \\\Leftrightarrow & 15x \color{red}{-10} & = &17 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-10} \color{blue}{+10} \color{blue}{+2x} & = &17 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+10} \\\Leftrightarrow & 15x+2x& = &17+10 \\\Leftrightarrow & 17x& = &27 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{27}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{27}{17} & & \\ & V = \left\{ \frac{27}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-x-1)& = & 2 \color{red}{-} (-14+x) \\\Leftrightarrow & -2x-2& = &2+14-x \\\Leftrightarrow & -2x \color{red}{-2} & = &16 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & -2x+x& = &16+2 \\\Leftrightarrow & -x& = &18 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{18}{ \color{red}{-1} } \\\Leftrightarrow & x = -18 & & \\ & V = \left\{ -18 \right\} & \\\end{align}\)