Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-x+2)& = & -4 \color{red}{-} (-10+x) \\\Leftrightarrow & -2x+4& = &-4+10-x \\\Leftrightarrow & -2x \color{red}{+4} & = &6 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -2x+x& = &6-4 \\\Leftrightarrow & -x& = &2 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{2}{ \color{red}{-1} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-4x+6)& = & 3 \color{red}{-} (-8-5x) \\\Leftrightarrow & -8x+12& = &3+8+5x \\\Leftrightarrow & -8x \color{red}{+12} & = &11 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &11 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & -8x-5x& = &11-12 \\\Leftrightarrow & -13x& = &-1 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-1}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{1}{13} & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-3x+1)& = & 7 \color{red}{+} (-9+x) \\\Leftrightarrow & -12x+4& = &7-9+x \\\Leftrightarrow & -12x \color{red}{+4} & = &-2 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & -12x-x& = &-2-4 \\\Leftrightarrow & -13x& = &-6 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-6}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{6}{13} & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-4x-5)& = & -10 \color{red}{-} (15+x) \\\Leftrightarrow & -12x-15& = &-10-15-x \\\Leftrightarrow & -12x \color{red}{-15} & = &-25 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &-25 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & -12x+x& = &-25+15 \\\Leftrightarrow & -11x& = &-10 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-10}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{10}{11} & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (4x-4)& = & -3 \color{red}{+} (13+x) \\\Leftrightarrow & 24x-24& = &-3+13+x \\\Leftrightarrow & 24x \color{red}{-24} & = &10 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 24x-x& = &10+24 \\\Leftrightarrow & 23x& = &34 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{34}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{34}{23} & & \\ & V = \left\{ \frac{34}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-3x+1)& = & -8 \color{red}{+} (-1+2x) \\\Leftrightarrow & -15x+5& = &-8-1+2x \\\Leftrightarrow & -15x \color{red}{+5} & = &-9 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+5} \color{blue}{-5} \color{blue}{-2x} & = &-9 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-5} \\\Leftrightarrow & -15x-2x& = &-9-5 \\\Leftrightarrow & -17x& = &-14 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-14}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{14}{17} & & \\ & V = \left\{ \frac{14}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-x+5)& = & 15 \color{red}{-} (-9-4x) \\\Leftrightarrow & -5x+25& = &15+9+4x \\\Leftrightarrow & -5x \color{red}{+25} & = &24 \color{red}{+4x} \\\Leftrightarrow & -5x \color{red}{+25} \color{blue}{-25} \color{blue}{-4x} & = &24 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-25} \\\Leftrightarrow & -5x-4x& = &24-25 \\\Leftrightarrow & -9x& = &-1 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-1}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{1}{9} & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (3x+6)& = & -1 \color{red}{-} (5-2x) \\\Leftrightarrow & 15x+30& = &-1-5+2x \\\Leftrightarrow & 15x \color{red}{+30} & = &-6 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+30} \color{blue}{-30} \color{blue}{-2x} & = &-6 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-30} \\\Leftrightarrow & 15x-2x& = &-6-30 \\\Leftrightarrow & 13x& = &-36 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-36}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-36}{13} & & \\ & V = \left\{ \frac{-36}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-6x+1)& = & 14 \color{red}{-} (6+x) \\\Leftrightarrow & -12x+2& = &14-6-x \\\Leftrightarrow & -12x \color{red}{+2} & = &8 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+2} \color{blue}{-2} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{-2} \\\Leftrightarrow & -12x+x& = &8-2 \\\Leftrightarrow & -11x& = &6 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{6}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-6}{11} & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-4x-4)& = & -14 \color{red}{+} (-7+x) \\\Leftrightarrow & -12x-12& = &-14-7+x \\\Leftrightarrow & -12x \color{red}{-12} & = &-21 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-21 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -12x-x& = &-21+12 \\\Leftrightarrow & -13x& = &-9 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-9}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{9}{13} & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (6x-1)& = & -3 \color{red}{+} (-4-5x) \\\Leftrightarrow & 18x-3& = &-3-4-5x \\\Leftrightarrow & 18x \color{red}{-3} & = &-7 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-3} \color{blue}{+3} \color{blue}{+5x} & = &-7 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+3} \\\Leftrightarrow & 18x+5x& = &-7+3 \\\Leftrightarrow & 23x& = &-4 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-4}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-4}{23} & & \\ & V = \left\{ \frac{-4}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (5x+6)& = & -10 \color{red}{-} (5+x) \\\Leftrightarrow & 25x+30& = &-10-5-x \\\Leftrightarrow & 25x \color{red}{+30} & = &-15 \color{red}{-x} \\\Leftrightarrow & 25x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &-15 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & 25x+x& = &-15-30 \\\Leftrightarrow & 26x& = &-45 \\\Leftrightarrow & \frac{26x}{ \color{red}{26} }& = &\frac{-45}{ \color{red}{26} } \\\Leftrightarrow & x = \frac{-45}{26} & & \\ & V = \left\{ \frac{-45}{26} \right\} & \\\end{align}\)