Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-6x+5)& = & 9 \color{red}{+} (-5+x) \\\Leftrightarrow & -18x+15& = &9-5+x \\\Leftrightarrow & -18x \color{red}{+15} & = &4 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & -18x-x& = &4-15 \\\Leftrightarrow & -19x& = &-11 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-11}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{11}{19} & & \\ & V = \left\{ \frac{11}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (2x+4)& = & 4 \color{red}{-} (-3+x) \\\Leftrightarrow & 6x+12& = &4+3-x \\\Leftrightarrow & 6x \color{red}{+12} & = &7 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 6x+x& = &7-12 \\\Leftrightarrow & 7x& = &-5 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-5}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-5}{7} & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (6x-1)& = & -3 \color{red}{+} (4+x) \\\Leftrightarrow & 12x-2& = &-3+4+x \\\Leftrightarrow & 12x \color{red}{-2} & = &1 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & 12x-x& = &1+2 \\\Leftrightarrow & 11x& = &3 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{3}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{3}{11} & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-2x-5)& = & 1 \color{red}{+} (2-5x) \\\Leftrightarrow & -6x-15& = &1+2-5x \\\Leftrightarrow & -6x \color{red}{-15} & = &3 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-15} \color{blue}{+15} \color{blue}{+5x} & = &3 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+15} \\\Leftrightarrow & -6x+5x& = &3+15 \\\Leftrightarrow & -x& = &18 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{18}{ \color{red}{-1} } \\\Leftrightarrow & x = -18 & & \\ & V = \left\{ -18 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (6x-1)& = & 14 \color{red}{+} (-13-5x) \\\Leftrightarrow & 18x-3& = &14-13-5x \\\Leftrightarrow & 18x \color{red}{-3} & = &1 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-3} \color{blue}{+3} \color{blue}{+5x} & = &1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+3} \\\Leftrightarrow & 18x+5x& = &1+3 \\\Leftrightarrow & 23x& = &4 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{4}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{4}{23} & & \\ & V = \left\{ \frac{4}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-4x+6)& = & -1 \color{red}{+} (-1+3x) \\\Leftrightarrow & -20x+30& = &-1-1+3x \\\Leftrightarrow & -20x \color{red}{+30} & = &-2 \color{red}{+3x} \\\Leftrightarrow & -20x \color{red}{+30} \color{blue}{-30} \color{blue}{-3x} & = &-2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-30} \\\Leftrightarrow & -20x-3x& = &-2-30 \\\Leftrightarrow & -23x& = &-32 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-32}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{32}{23} & & \\ & V = \left\{ \frac{32}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-3x-2)& = & -9 \color{red}{+} (8+2x) \\\Leftrightarrow & -9x-6& = &-9+8+2x \\\Leftrightarrow & -9x \color{red}{-6} & = &-1 \color{red}{+2x} \\\Leftrightarrow & -9x \color{red}{-6} \color{blue}{+6} \color{blue}{-2x} & = &-1 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+6} \\\Leftrightarrow & -9x-2x& = &-1+6 \\\Leftrightarrow & -11x& = &5 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{5}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-5}{11} & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-5x+6)& = & 8 \color{red}{+} (11+x) \\\Leftrightarrow & -30x+36& = &8+11+x \\\Leftrightarrow & -30x \color{red}{+36} & = &19 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & -30x-x& = &19-36 \\\Leftrightarrow & -31x& = &-17 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-17}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{17}{31} & & \\ & V = \left\{ \frac{17}{31} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (x-7)& = & -4 \color{red}{+} (-6+x) \\\Leftrightarrow & 3x-21& = &-4-6+x \\\Leftrightarrow & 3x \color{red}{-21} & = &-10 \color{red}{+x} \\\Leftrightarrow & 3x \color{red}{-21} \color{blue}{+21} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{+21} \\\Leftrightarrow & 3x-x& = &-10+21 \\\Leftrightarrow & 2x& = &11 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{11}{ \color{red}{2} } \\\Leftrightarrow & x = \frac{11}{2} & & \\ & V = \left\{ \frac{11}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-5x+4)& = & 10 \color{red}{+} (-7+x) \\\Leftrightarrow & -15x+12& = &10-7+x \\\Leftrightarrow & -15x \color{red}{+12} & = &3 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -15x-x& = &3-12 \\\Leftrightarrow & -16x& = &-9 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{-9}{ \color{red}{-16} } \\\Leftrightarrow & x = \frac{9}{16} & & \\ & V = \left\{ \frac{9}{16} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (3x-4)& = & 6 \color{red}{-} (-14+x) \\\Leftrightarrow & 6x-8& = &6+14-x \\\Leftrightarrow & 6x \color{red}{-8} & = &20 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 6x+x& = &20+8 \\\Leftrightarrow & 7x& = &28 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{28}{ \color{red}{7} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-6x+7)& = & -3 \color{red}{+} (-15+x) \\\Leftrightarrow & -12x+14& = &-3-15+x \\\Leftrightarrow & -12x \color{red}{+14} & = &-18 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+14} \color{blue}{-14} \color{blue}{-x} & = &-18 \color{red}{+x} \color{blue}{-x} \color{blue}{-14} \\\Leftrightarrow & -12x-x& = &-18-14 \\\Leftrightarrow & -13x& = &-32 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-32}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{32}{13} & & \\ & V = \left\{ \frac{32}{13} \right\} & \\\end{align}\)