Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-5x-4)& = & -13 \color{red}{+} (7-4x) \\\Leftrightarrow & -25x-20& = &-13+7-4x \\\Leftrightarrow & -25x \color{red}{-20} & = &-6 \color{red}{-4x} \\\Leftrightarrow & -25x \color{red}{-20} \color{blue}{+20} \color{blue}{+4x} & = &-6 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+20} \\\Leftrightarrow & -25x+4x& = &-6+20 \\\Leftrightarrow & -21x& = &14 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{14}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-2}{3} & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-x-6)& = & 5 \color{red}{-} (-13-5x) \\\Leftrightarrow & -6x-36& = &5+13+5x \\\Leftrightarrow & -6x \color{red}{-36} & = &18 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-36} \color{blue}{+36} \color{blue}{-5x} & = &18 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+36} \\\Leftrightarrow & -6x-5x& = &18+36 \\\Leftrightarrow & -11x& = &54 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{54}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-54}{11} & & \\ & V = \left\{ \frac{-54}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (5x-2)& = & -15 \color{red}{-} (-4+x) \\\Leftrightarrow & 20x-8& = &-15+4-x \\\Leftrightarrow & 20x \color{red}{-8} & = &-11 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 20x+x& = &-11+8 \\\Leftrightarrow & 21x& = &-3 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-3}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-1}{7} & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-x+3)& = & 10 \color{red}{+} (3+x) \\\Leftrightarrow & -2x+6& = &10+3+x \\\Leftrightarrow & -2x \color{red}{+6} & = &13 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -2x-x& = &13-6 \\\Leftrightarrow & -3x& = &7 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{7}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-7}{3} & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-2x-4)& = & -2 \color{red}{-} (2+x) \\\Leftrightarrow & -12x-24& = &-2-2-x \\\Leftrightarrow & -12x \color{red}{-24} & = &-4 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -12x+x& = &-4+24 \\\Leftrightarrow & -11x& = &20 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{20}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-20}{11} & & \\ & V = \left\{ \frac{-20}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (3x+1)& = & 13 \color{red}{+} (-7+4x) \\\Leftrightarrow & 15x+5& = &13-7+4x \\\Leftrightarrow & 15x \color{red}{+5} & = &6 \color{red}{+4x} \\\Leftrightarrow & 15x \color{red}{+5} \color{blue}{-5} \color{blue}{-4x} & = &6 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-5} \\\Leftrightarrow & 15x-4x& = &6-5 \\\Leftrightarrow & 11x& = &1 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{1}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{1}{11} & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (x-3)& = & -3 \color{red}{+} (11+x) \\\Leftrightarrow & 6x-18& = &-3+11+x \\\Leftrightarrow & 6x \color{red}{-18} & = &8 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & 6x-x& = &8+18 \\\Leftrightarrow & 5x& = &26 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{26}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{26}{5} & & \\ & V = \left\{ \frac{26}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-5x-7)& = & 2 \color{red}{+} (13+4x) \\\Leftrightarrow & -15x-21& = &2+13+4x \\\Leftrightarrow & -15x \color{red}{-21} & = &15 \color{red}{+4x} \\\Leftrightarrow & -15x \color{red}{-21} \color{blue}{+21} \color{blue}{-4x} & = &15 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+21} \\\Leftrightarrow & -15x-4x& = &15+21 \\\Leftrightarrow & -19x& = &36 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{36}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-36}{19} & & \\ & V = \left\{ \frac{-36}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-6x+4)& = & 14 \color{red}{+} (8+x) \\\Leftrightarrow & -12x+8& = &14+8+x \\\Leftrightarrow & -12x \color{red}{+8} & = &22 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &22 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -12x-x& = &22-8 \\\Leftrightarrow & -13x& = &14 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{14}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-14}{13} & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (2x+7)& = & -10 \color{red}{-} (-13+x) \\\Leftrightarrow & 10x+35& = &-10+13-x \\\Leftrightarrow & 10x \color{red}{+35} & = &3 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{+35} \color{blue}{-35} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{-35} \\\Leftrightarrow & 10x+x& = &3-35 \\\Leftrightarrow & 11x& = &-32 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-32}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-32}{11} & & \\ & V = \left\{ \frac{-32}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (x-5)& = & -9 \color{red}{-} (7-3x) \\\Leftrightarrow & 4x-20& = &-9-7+3x \\\Leftrightarrow & 4x \color{red}{-20} & = &-16 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-20} \color{blue}{+20} \color{blue}{-3x} & = &-16 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+20} \\\Leftrightarrow & 4x-3x& = &-16+20 \\\Leftrightarrow & x& = &4 \\ & V = \left\{ 4 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (4x+3)& = & 11 \color{red}{+} (4-5x) \\\Leftrightarrow & 8x+6& = &11+4-5x \\\Leftrightarrow & 8x \color{red}{+6} & = &15 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &15 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & 8x+5x& = &15-6 \\\Leftrightarrow & 13x& = &9 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{9}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{9}{13} & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)