Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-x+4)& = & 14 \color{red}{-} (-4-5x) \\\Leftrightarrow & -6x+24& = &14+4+5x \\\Leftrightarrow & -6x \color{red}{+24} & = &18 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+24} \color{blue}{-24} \color{blue}{-5x} & = &18 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-24} \\\Leftrightarrow & -6x-5x& = &18-24 \\\Leftrightarrow & -11x& = &-6 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-6}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{6}{11} & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-2x+7)& = & 11 \color{red}{-} (2-3x) \\\Leftrightarrow & -10x+35& = &11-2+3x \\\Leftrightarrow & -10x \color{red}{+35} & = &9 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+35} \color{blue}{-35} \color{blue}{-3x} & = &9 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-35} \\\Leftrightarrow & -10x-3x& = &9-35 \\\Leftrightarrow & -13x& = &-26 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-26}{ \color{red}{-13} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (5x-2)& = & -15 \color{red}{+} (14+2x) \\\Leftrightarrow & 15x-6& = &-15+14+2x \\\Leftrightarrow & 15x \color{red}{-6} & = &-1 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{-6} \color{blue}{+6} \color{blue}{-2x} & = &-1 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+6} \\\Leftrightarrow & 15x-2x& = &-1+6 \\\Leftrightarrow & 13x& = &5 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{5}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{5}{13} & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-x-6)& = & 2 \color{red}{+} (8-3x) \\\Leftrightarrow & -4x-24& = &2+8-3x \\\Leftrightarrow & -4x \color{red}{-24} & = &10 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-24} \color{blue}{+24} \color{blue}{+3x} & = &10 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+24} \\\Leftrightarrow & -4x+3x& = &10+24 \\\Leftrightarrow & -x& = &34 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{34}{ \color{red}{-1} } \\\Leftrightarrow & x = -34 & & \\ & V = \left\{ -34 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (x+6)& = & -12 \color{red}{+} (-2-3x) \\\Leftrightarrow & 4x+24& = &-12-2-3x \\\Leftrightarrow & 4x \color{red}{+24} & = &-14 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+24} \color{blue}{-24} \color{blue}{+3x} & = &-14 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-24} \\\Leftrightarrow & 4x+3x& = &-14-24 \\\Leftrightarrow & 7x& = &-38 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-38}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-38}{7} & & \\ & V = \left\{ \frac{-38}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-x-6)& = & 8 \color{red}{+} (-14+x) \\\Leftrightarrow & -6x-36& = &8-14+x \\\Leftrightarrow & -6x \color{red}{-36} & = &-6 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & -6x-x& = &-6+36 \\\Leftrightarrow & -7x& = &30 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{30}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-30}{7} & & \\ & V = \left\{ \frac{-30}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-6x-7)& = & 14 \color{red}{+} (4-5x) \\\Leftrightarrow & -18x-21& = &14+4-5x \\\Leftrightarrow & -18x \color{red}{-21} & = &18 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-21} \color{blue}{+21} \color{blue}{+5x} & = &18 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+21} \\\Leftrightarrow & -18x+5x& = &18+21 \\\Leftrightarrow & -13x& = &39 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{39}{ \color{red}{-13} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (4x-3)& = & 6 \color{red}{-} (11-5x) \\\Leftrightarrow & 16x-12& = &6-11+5x \\\Leftrightarrow & 16x \color{red}{-12} & = &-5 \color{red}{+5x} \\\Leftrightarrow & 16x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &-5 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & 16x-5x& = &-5+12 \\\Leftrightarrow & 11x& = &7 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{7}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{7}{11} & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-2x+1)& = & 1 \color{red}{-} (-13-5x) \\\Leftrightarrow & -8x+4& = &1+13+5x \\\Leftrightarrow & -8x \color{red}{+4} & = &14 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{+4} \color{blue}{-4} \color{blue}{-5x} & = &14 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-4} \\\Leftrightarrow & -8x-5x& = &14-4 \\\Leftrightarrow & -13x& = &10 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{10}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-10}{13} & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-5x-4)& = & 12 \color{red}{-} (-8+x) \\\Leftrightarrow & -10x-8& = &12+8-x \\\Leftrightarrow & -10x \color{red}{-8} & = &20 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & -10x+x& = &20+8 \\\Leftrightarrow & -9x& = &28 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{28}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-28}{9} & & \\ & V = \left\{ \frac{-28}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (2x+6)& = & 9 \color{red}{+} (-4+x) \\\Leftrightarrow & 4x+12& = &9-4+x \\\Leftrightarrow & 4x \color{red}{+12} & = &5 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 4x-x& = &5-12 \\\Leftrightarrow & 3x& = &-7 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-7}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-7}{3} & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-2x-4)& = & 2 \color{red}{-} (7-5x) \\\Leftrightarrow & -6x-12& = &2-7+5x \\\Leftrightarrow & -6x \color{red}{-12} & = &-5 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &-5 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & -6x-5x& = &-5+12 \\\Leftrightarrow & -11x& = &7 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{7}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-7}{11} & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)