Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-x+7)& = & 10 \color{red}{-} (4+x) \\\Leftrightarrow & -5x+35& = &10-4-x \\\Leftrightarrow & -5x \color{red}{+35} & = &6 \color{red}{-x} \\\Leftrightarrow & -5x \color{red}{+35} \color{blue}{-35} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{-35} \\\Leftrightarrow & -5x+x& = &6-35 \\\Leftrightarrow & -4x& = &-29 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{-29}{ \color{red}{-4} } \\\Leftrightarrow & x = \frac{29}{4} & & \\ & V = \left\{ \frac{29}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (3x+5)& = & -12 \color{red}{+} (-9+x) \\\Leftrightarrow & 12x+20& = &-12-9+x \\\Leftrightarrow & 12x \color{red}{+20} & = &-21 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &-21 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 12x-x& = &-21-20 \\\Leftrightarrow & 11x& = &-41 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-41}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-41}{11} & & \\ & V = \left\{ \frac{-41}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (x-4)& = & 6 \color{red}{-} (-9-5x) \\\Leftrightarrow & 6x-24& = &6+9+5x \\\Leftrightarrow & 6x \color{red}{-24} & = &15 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-24} \color{blue}{+24} \color{blue}{-5x} & = &15 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+24} \\\Leftrightarrow & 6x-5x& = &15+24 \\\Leftrightarrow & x& = &39 \\ & V = \left\{ 39 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-5x-2)& = & 6 \color{red}{+} (-11+3x) \\\Leftrightarrow & -20x-8& = &6-11+3x \\\Leftrightarrow & -20x \color{red}{-8} & = &-5 \color{red}{+3x} \\\Leftrightarrow & -20x \color{red}{-8} \color{blue}{+8} \color{blue}{-3x} & = &-5 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+8} \\\Leftrightarrow & -20x-3x& = &-5+8 \\\Leftrightarrow & -23x& = &3 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{3}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-3}{23} & & \\ & V = \left\{ \frac{-3}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (5x-3)& = & -11 \color{red}{-} (15+x) \\\Leftrightarrow & 25x-15& = &-11-15-x \\\Leftrightarrow & 25x \color{red}{-15} & = &-26 \color{red}{-x} \\\Leftrightarrow & 25x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &-26 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & 25x+x& = &-26+15 \\\Leftrightarrow & 26x& = &-11 \\\Leftrightarrow & \frac{26x}{ \color{red}{26} }& = &\frac{-11}{ \color{red}{26} } \\\Leftrightarrow & x = \frac{-11}{26} & & \\ & V = \left\{ \frac{-11}{26} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-5x-5)& = & 9 \color{red}{+} (-8-3x) \\\Leftrightarrow & -10x-10& = &9-8-3x \\\Leftrightarrow & -10x \color{red}{-10} & = &1 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{-10} \color{blue}{+10} \color{blue}{+3x} & = &1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+10} \\\Leftrightarrow & -10x+3x& = &1+10 \\\Leftrightarrow & -7x& = &11 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{11}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-11}{7} & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-6x+1)& = & 3 \color{red}{+} (-5+x) \\\Leftrightarrow & -36x+6& = &3-5+x \\\Leftrightarrow & -36x \color{red}{+6} & = &-2 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -36x-x& = &-2-6 \\\Leftrightarrow & -37x& = &-8 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{-8}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{8}{37} & & \\ & V = \left\{ \frac{8}{37} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-x-2)& = & 9 \color{red}{-} (-12+3x) \\\Leftrightarrow & -2x-4& = &9+12-3x \\\Leftrightarrow & -2x \color{red}{-4} & = &21 \color{red}{-3x} \\\Leftrightarrow & -2x \color{red}{-4} \color{blue}{+4} \color{blue}{+3x} & = &21 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+4} \\\Leftrightarrow & -2x+3x& = &21+4 \\\Leftrightarrow & x& = &25 \\ & V = \left\{ 25 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (4x-6)& = & -6 \color{red}{+} (14+x) \\\Leftrightarrow & 8x-12& = &-6+14+x \\\Leftrightarrow & 8x \color{red}{-12} & = &8 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 8x-x& = &8+12 \\\Leftrightarrow & 7x& = &20 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{20}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{20}{7} & & \\ & V = \left\{ \frac{20}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (4x-1)& = & 5 \color{red}{-} (14+x) \\\Leftrightarrow & 12x-3& = &5-14-x \\\Leftrightarrow & 12x \color{red}{-3} & = &-9 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-3} \color{blue}{+3} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{+3} \\\Leftrightarrow & 12x+x& = &-9+3 \\\Leftrightarrow & 13x& = &-6 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-6}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-6}{13} & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-4x+2)& = & -15 \color{red}{-} (-13+x) \\\Leftrightarrow & -20x+10& = &-15+13-x \\\Leftrightarrow & -20x \color{red}{+10} & = &-2 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & -20x+x& = &-2-10 \\\Leftrightarrow & -19x& = &-12 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-12}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{12}{19} & & \\ & V = \left\{ \frac{12}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-2x-5)& = & -5 \color{red}{+} (15+x) \\\Leftrightarrow & -6x-15& = &-5+15+x \\\Leftrightarrow & -6x \color{red}{-15} & = &10 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & -6x-x& = &10+15 \\\Leftrightarrow & -7x& = &25 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{25}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-25}{7} & & \\ & V = \left\{ \frac{-25}{7} \right\} & \\\end{align}\)