Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-6x+5)& = & -9 \color{red}{-} (8+x) \\\Leftrightarrow & -36x+30& = &-9-8-x \\\Leftrightarrow & -36x \color{red}{+30} & = &-17 \color{red}{-x} \\\Leftrightarrow & -36x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & -36x+x& = &-17-30 \\\Leftrightarrow & -35x& = &-47 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = &\frac{-47}{ \color{red}{-35} } \\\Leftrightarrow & x = \frac{47}{35} & & \\ & V = \left\{ \frac{47}{35} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-3x+7)& = & -13 \color{red}{+} (14-2x) \\\Leftrightarrow & -9x+21& = &-13+14-2x \\\Leftrightarrow & -9x \color{red}{+21} & = &1 \color{red}{-2x} \\\Leftrightarrow & -9x \color{red}{+21} \color{blue}{-21} \color{blue}{+2x} & = &1 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-21} \\\Leftrightarrow & -9x+2x& = &1-21 \\\Leftrightarrow & -7x& = &-20 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-20}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{20}{7} & & \\ & V = \left\{ \frac{20}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (x+4)& = & 8 \color{red}{-} (-12+x) \\\Leftrightarrow & 2x+8& = &8+12-x \\\Leftrightarrow & 2x \color{red}{+8} & = &20 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 2x+x& = &20-8 \\\Leftrightarrow & 3x& = &12 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{12}{ \color{red}{3} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (3x-6)& = & 1 \color{red}{+} (2-2x) \\\Leftrightarrow & 9x-18& = &1+2-2x \\\Leftrightarrow & 9x \color{red}{-18} & = &3 \color{red}{-2x} \\\Leftrightarrow & 9x \color{red}{-18} \color{blue}{+18} \color{blue}{+2x} & = &3 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+18} \\\Leftrightarrow & 9x+2x& = &3+18 \\\Leftrightarrow & 11x& = &21 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{21}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{21}{11} & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-6x-5)& = & 5 \color{red}{+} (-13-5x) \\\Leftrightarrow & -18x-15& = &5-13-5x \\\Leftrightarrow & -18x \color{red}{-15} & = &-8 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-15} \color{blue}{+15} \color{blue}{+5x} & = &-8 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+15} \\\Leftrightarrow & -18x+5x& = &-8+15 \\\Leftrightarrow & -13x& = &7 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{7}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-7}{13} & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (3x-3)& = & -15 \color{red}{+} (-4+x) \\\Leftrightarrow & 18x-18& = &-15-4+x \\\Leftrightarrow & 18x \color{red}{-18} & = &-19 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & 18x-x& = &-19+18 \\\Leftrightarrow & 17x& = &-1 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-1}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-1}{17} & & \\ & V = \left\{ \frac{-1}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (5x+5)& = & 4 \color{red}{-} (15-3x) \\\Leftrightarrow & 10x+10& = &4-15+3x \\\Leftrightarrow & 10x \color{red}{+10} & = &-11 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+10} \color{blue}{-10} \color{blue}{-3x} & = &-11 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-10} \\\Leftrightarrow & 10x-3x& = &-11-10 \\\Leftrightarrow & 7x& = &-21 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-21}{ \color{red}{7} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (4x-2)& = & -1 \color{red}{+} (-4+x) \\\Leftrightarrow & 24x-12& = &-1-4+x \\\Leftrightarrow & 24x \color{red}{-12} & = &-5 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 24x-x& = &-5+12 \\\Leftrightarrow & 23x& = &7 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{7}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{7}{23} & & \\ & V = \left\{ \frac{7}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (x-6)& = & -12 \color{red}{+} (-1+4x) \\\Leftrightarrow & 3x-18& = &-12-1+4x \\\Leftrightarrow & 3x \color{red}{-18} & = &-13 \color{red}{+4x} \\\Leftrightarrow & 3x \color{red}{-18} \color{blue}{+18} \color{blue}{-4x} & = &-13 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+18} \\\Leftrightarrow & 3x-4x& = &-13+18 \\\Leftrightarrow & -x& = &5 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{5}{ \color{red}{-1} } \\\Leftrightarrow & x = -5 & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-5x-7)& = & -5 \color{red}{-} (-5+x) \\\Leftrightarrow & -20x-28& = &-5+5-x \\\Leftrightarrow & -20x \color{red}{-28} & = &0 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-28} \color{blue}{+28} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+28} \\\Leftrightarrow & -20x+x& = &0+28 \\\Leftrightarrow & -19x& = &28 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{28}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-28}{19} & & \\ & V = \left\{ \frac{-28}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-5x-3)& = & 13 \color{red}{+} (-15-3x) \\\Leftrightarrow & -10x-6& = &13-15-3x \\\Leftrightarrow & -10x \color{red}{-6} & = &-2 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{-6} \color{blue}{+6} \color{blue}{+3x} & = &-2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+6} \\\Leftrightarrow & -10x+3x& = &-2+6 \\\Leftrightarrow & -7x& = &4 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{4}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-4}{7} & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-2x-6)& = & -15 \color{red}{+} (2+x) \\\Leftrightarrow & -6x-18& = &-15+2+x \\\Leftrightarrow & -6x \color{red}{-18} & = &-13 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & -6x-x& = &-13+18 \\\Leftrightarrow & -7x& = &5 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{5}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-5}{7} & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)