Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-2x+1)& = & 6 \color{red}{-} (12+x) \\\Leftrightarrow & -6x+3& = &6-12-x \\\Leftrightarrow & -6x \color{red}{+3} & = &-6 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+3} \color{blue}{-3} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{-3} \\\Leftrightarrow & -6x+x& = &-6-3 \\\Leftrightarrow & -5x& = &-9 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-9}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{9}{5} & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (5x+5)& = & -12 \color{red}{+} (8+x) \\\Leftrightarrow & 20x+20& = &-12+8+x \\\Leftrightarrow & 20x \color{red}{+20} & = &-4 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 20x-x& = &-4-20 \\\Leftrightarrow & 19x& = &-24 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-24}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-24}{19} & & \\ & V = \left\{ \frac{-24}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-x-5)& = & 15 \color{red}{+} (-7+4x) \\\Leftrightarrow & -5x-25& = &15-7+4x \\\Leftrightarrow & -5x \color{red}{-25} & = &8 \color{red}{+4x} \\\Leftrightarrow & -5x \color{red}{-25} \color{blue}{+25} \color{blue}{-4x} & = &8 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+25} \\\Leftrightarrow & -5x-4x& = &8+25 \\\Leftrightarrow & -9x& = &33 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{33}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-11}{3} & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (x-4)& = & 2 \color{red}{-} (-11+x) \\\Leftrightarrow & 5x-20& = &2+11-x \\\Leftrightarrow & 5x \color{red}{-20} & = &13 \color{red}{-x} \\\Leftrightarrow & 5x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & 5x+x& = &13+20 \\\Leftrightarrow & 6x& = &33 \\\Leftrightarrow & \frac{6x}{ \color{red}{6} }& = &\frac{33}{ \color{red}{6} } \\\Leftrightarrow & x = \frac{11}{2} & & \\ & V = \left\{ \frac{11}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (6x+4)& = & -14 \color{red}{+} (-9+x) \\\Leftrightarrow & 12x+8& = &-14-9+x \\\Leftrightarrow & 12x \color{red}{+8} & = &-23 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-23 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 12x-x& = &-23-8 \\\Leftrightarrow & 11x& = &-31 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-31}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-31}{11} & & \\ & V = \left\{ \frac{-31}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-4x-1)& = & -6 \color{red}{+} (7+x) \\\Leftrightarrow & -12x-3& = &-6+7+x \\\Leftrightarrow & -12x \color{red}{-3} & = &1 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-3} \color{blue}{+3} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+3} \\\Leftrightarrow & -12x-x& = &1+3 \\\Leftrightarrow & -13x& = &4 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{4}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-4}{13} & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (4x-3)& = & -12 \color{red}{+} (15+3x) \\\Leftrightarrow & 20x-15& = &-12+15+3x \\\Leftrightarrow & 20x \color{red}{-15} & = &3 \color{red}{+3x} \\\Leftrightarrow & 20x \color{red}{-15} \color{blue}{+15} \color{blue}{-3x} & = &3 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+15} \\\Leftrightarrow & 20x-3x& = &3+15 \\\Leftrightarrow & 17x& = &18 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{18}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{18}{17} & & \\ & V = \left\{ \frac{18}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (3x-7)& = & 7 \color{red}{+} (12+x) \\\Leftrightarrow & 12x-28& = &7+12+x \\\Leftrightarrow & 12x \color{red}{-28} & = &19 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & 12x-x& = &19+28 \\\Leftrightarrow & 11x& = &47 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{47}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{47}{11} & & \\ & V = \left\{ \frac{47}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-4x+1)& = & 14 \color{red}{-} (3+x) \\\Leftrightarrow & -20x+5& = &14-3-x \\\Leftrightarrow & -20x \color{red}{+5} & = &11 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+5} \color{blue}{-5} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{-5} \\\Leftrightarrow & -20x+x& = &11-5 \\\Leftrightarrow & -19x& = &6 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{6}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-6}{19} & & \\ & V = \left\{ \frac{-6}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (5x+7)& = & -9 \color{red}{+} (-10-3x) \\\Leftrightarrow & 25x+35& = &-9-10-3x \\\Leftrightarrow & 25x \color{red}{+35} & = &-19 \color{red}{-3x} \\\Leftrightarrow & 25x \color{red}{+35} \color{blue}{-35} \color{blue}{+3x} & = &-19 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-35} \\\Leftrightarrow & 25x+3x& = &-19-35 \\\Leftrightarrow & 28x& = &-54 \\\Leftrightarrow & \frac{28x}{ \color{red}{28} }& = &\frac{-54}{ \color{red}{28} } \\\Leftrightarrow & x = \frac{-27}{14} & & \\ & V = \left\{ \frac{-27}{14} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (x+6)& = & 2 \color{red}{-} (7+x) \\\Leftrightarrow & 3x+18& = &2-7-x \\\Leftrightarrow & 3x \color{red}{+18} & = &-5 \color{red}{-x} \\\Leftrightarrow & 3x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 3x+x& = &-5-18 \\\Leftrightarrow & 4x& = &-23 \\\Leftrightarrow & \frac{4x}{ \color{red}{4} }& = &\frac{-23}{ \color{red}{4} } \\\Leftrightarrow & x = \frac{-23}{4} & & \\ & V = \left\{ \frac{-23}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (6x-7)& = & -1 \color{red}{-} (11+x) \\\Leftrightarrow & 30x-35& = &-1-11-x \\\Leftrightarrow & 30x \color{red}{-35} & = &-12 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-35} \color{blue}{+35} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{+35} \\\Leftrightarrow & 30x+x& = &-12+35 \\\Leftrightarrow & 31x& = &23 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{23}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{23}{31} & & \\ & V = \left\{ \frac{23}{31} \right\} & \\\end{align}\)