Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (6x-6)& = & -10 \color{red}{+} (7+x) \\\Leftrightarrow & 36x-36& = &-10+7+x \\\Leftrightarrow & 36x \color{red}{-36} & = &-3 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & 36x-x& = &-3+36 \\\Leftrightarrow & 35x& = &33 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{33}{ \color{red}{35} } \\\Leftrightarrow & x = \frac{33}{35} & & \\ & V = \left\{ \frac{33}{35} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-3x-4)& = & -12 \color{red}{-} (11-2x) \\\Leftrightarrow & -15x-20& = &-12-11+2x \\\Leftrightarrow & -15x \color{red}{-20} & = &-23 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{-20} \color{blue}{+20} \color{blue}{-2x} & = &-23 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+20} \\\Leftrightarrow & -15x-2x& = &-23+20 \\\Leftrightarrow & -17x& = &-3 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-3}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{3}{17} & & \\ & V = \left\{ \frac{3}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (2x-2)& = & 10 \color{red}{+} (-12+x) \\\Leftrightarrow & 12x-12& = &10-12+x \\\Leftrightarrow & 12x \color{red}{-12} & = &-2 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 12x-x& = &-2+12 \\\Leftrightarrow & 11x& = &10 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{10}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{10}{11} & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-6x-6)& = & -7 \color{red}{+} (-11-5x) \\\Leftrightarrow & -18x-18& = &-7-11-5x \\\Leftrightarrow & -18x \color{red}{-18} & = &-18 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-18} \color{blue}{+18} \color{blue}{+5x} & = &-18 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+18} \\\Leftrightarrow & -18x+5x& = &-18+18 \\\Leftrightarrow & -13x& = &0 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{0}{ \color{red}{-13} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-x+6)& = & -6 \color{red}{-} (10-2x) \\\Leftrightarrow & -3x+18& = &-6-10+2x \\\Leftrightarrow & -3x \color{red}{+18} & = &-16 \color{red}{+2x} \\\Leftrightarrow & -3x \color{red}{+18} \color{blue}{-18} \color{blue}{-2x} & = &-16 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-18} \\\Leftrightarrow & -3x-2x& = &-16-18 \\\Leftrightarrow & -5x& = &-34 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-34}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{34}{5} & & \\ & V = \left\{ \frac{34}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (5x+6)& = & -10 \color{red}{+} (8+x) \\\Leftrightarrow & 30x+36& = &-10+8+x \\\Leftrightarrow & 30x \color{red}{+36} & = &-2 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & 30x-x& = &-2-36 \\\Leftrightarrow & 29x& = &-38 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-38}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-38}{29} & & \\ & V = \left\{ \frac{-38}{29} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (3x+1)& = & -12 \color{red}{+} (12+x) \\\Leftrightarrow & 6x+2& = &-12+12+x \\\Leftrightarrow & 6x \color{red}{+2} & = &0 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+2} \color{blue}{-2} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-2} \\\Leftrightarrow & 6x-x& = &0-2 \\\Leftrightarrow & 5x& = &-2 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-2}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-2}{5} & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-x-7)& = & -9 \color{red}{-} (6-5x) \\\Leftrightarrow & -6x-42& = &-9-6+5x \\\Leftrightarrow & -6x \color{red}{-42} & = &-15 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-42} \color{blue}{+42} \color{blue}{-5x} & = &-15 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+42} \\\Leftrightarrow & -6x-5x& = &-15+42 \\\Leftrightarrow & -11x& = &27 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{27}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-27}{11} & & \\ & V = \left\{ \frac{-27}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (6x+5)& = & -9 \color{red}{+} (-6+x) \\\Leftrightarrow & 24x+20& = &-9-6+x \\\Leftrightarrow & 24x \color{red}{+20} & = &-15 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 24x-x& = &-15-20 \\\Leftrightarrow & 23x& = &-35 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-35}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-35}{23} & & \\ & V = \left\{ \frac{-35}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-3x-7)& = & 5 \color{red}{-} (15+x) \\\Leftrightarrow & -6x-14& = &5-15-x \\\Leftrightarrow & -6x \color{red}{-14} & = &-10 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-14} \color{blue}{+14} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{+14} \\\Leftrightarrow & -6x+x& = &-10+14 \\\Leftrightarrow & -5x& = &4 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{4}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-4}{5} & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (4x-2)& = & -3 \color{red}{+} (14+x) \\\Leftrightarrow & 20x-10& = &-3+14+x \\\Leftrightarrow & 20x \color{red}{-10} & = &11 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & 20x-x& = &11+10 \\\Leftrightarrow & 19x& = &21 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{21}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{21}{19} & & \\ & V = \left\{ \frac{21}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (2x+6)& = & 9 \color{red}{+} (-6+x) \\\Leftrightarrow & 12x+36& = &9-6+x \\\Leftrightarrow & 12x \color{red}{+36} & = &3 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & 12x-x& = &3-36 \\\Leftrightarrow & 11x& = &-33 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-33}{ \color{red}{11} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)