Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (4x+2)& = & -13 \color{red}{+} (-1+x) \\\Leftrightarrow & 20x+10& = &-13-1+x \\\Leftrightarrow & 20x \color{red}{+10} & = &-14 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & 20x-x& = &-14-10 \\\Leftrightarrow & 19x& = &-24 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-24}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-24}{19} & & \\ & V = \left\{ \frac{-24}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (5x+5)& = & -6 \color{red}{+} (8-3x) \\\Leftrightarrow & 10x+10& = &-6+8-3x \\\Leftrightarrow & 10x \color{red}{+10} & = &2 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+10} \color{blue}{-10} \color{blue}{+3x} & = &2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-10} \\\Leftrightarrow & 10x+3x& = &2-10 \\\Leftrightarrow & 13x& = &-8 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-8}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-8}{13} & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-2x-7)& = & -2 \color{red}{-} (-2-5x) \\\Leftrightarrow & -6x-21& = &-2+2+5x \\\Leftrightarrow & -6x \color{red}{-21} & = &0 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-21} \color{blue}{+21} \color{blue}{-5x} & = &0 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+21} \\\Leftrightarrow & -6x-5x& = &0+21 \\\Leftrightarrow & -11x& = &21 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{21}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-21}{11} & & \\ & V = \left\{ \frac{-21}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-5x-1)& = & -14 \color{red}{+} (-4+x) \\\Leftrightarrow & -30x-6& = &-14-4+x \\\Leftrightarrow & -30x \color{red}{-6} & = &-18 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-18 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -30x-x& = &-18+6 \\\Leftrightarrow & -31x& = &-12 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-12}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{12}{31} & & \\ & V = \left\{ \frac{12}{31} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-2x-5)& = & 15 \color{red}{+} (-4-3x) \\\Leftrightarrow & -4x-10& = &15-4-3x \\\Leftrightarrow & -4x \color{red}{-10} & = &11 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-10} \color{blue}{+10} \color{blue}{+3x} & = &11 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+10} \\\Leftrightarrow & -4x+3x& = &11+10 \\\Leftrightarrow & -x& = &21 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{21}{ \color{red}{-1} } \\\Leftrightarrow & x = -21 & & \\ & V = \left\{ -21 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (x-5)& = & 7 \color{red}{-} (-6+x) \\\Leftrightarrow & 4x-20& = &7+6-x \\\Leftrightarrow & 4x \color{red}{-20} & = &13 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & 4x+x& = &13+20 \\\Leftrightarrow & 5x& = &33 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{33}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{33}{5} & & \\ & V = \left\{ \frac{33}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-x-7)& = & 7 \color{red}{-} (-7+x) \\\Leftrightarrow & -2x-14& = &7+7-x \\\Leftrightarrow & -2x \color{red}{-14} & = &14 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{-14} \color{blue}{+14} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{+14} \\\Leftrightarrow & -2x+x& = &14+14 \\\Leftrightarrow & -x& = &28 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{28}{ \color{red}{-1} } \\\Leftrightarrow & x = -28 & & \\ & V = \left\{ -28 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (6x+5)& = & -12 \color{red}{+} (7-5x) \\\Leftrightarrow & 18x+15& = &-12+7-5x \\\Leftrightarrow & 18x \color{red}{+15} & = &-5 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{+15} \color{blue}{-15} \color{blue}{+5x} & = &-5 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-15} \\\Leftrightarrow & 18x+5x& = &-5-15 \\\Leftrightarrow & 23x& = &-20 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-20}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-20}{23} & & \\ & V = \left\{ \frac{-20}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (5x-5)& = & 11 \color{red}{+} (8+x) \\\Leftrightarrow & 20x-20& = &11+8+x \\\Leftrightarrow & 20x \color{red}{-20} & = &19 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & 20x-x& = &19+20 \\\Leftrightarrow & 19x& = &39 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{39}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{39}{19} & & \\ & V = \left\{ \frac{39}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (x-7)& = & -2 \color{red}{-} (-9-2x) \\\Leftrightarrow & 5x-35& = &-2+9+2x \\\Leftrightarrow & 5x \color{red}{-35} & = &7 \color{red}{+2x} \\\Leftrightarrow & 5x \color{red}{-35} \color{blue}{+35} \color{blue}{-2x} & = &7 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+35} \\\Leftrightarrow & 5x-2x& = &7+35 \\\Leftrightarrow & 3x& = &42 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{42}{ \color{red}{3} } \\\Leftrightarrow & x = 14 & & \\ & V = \left\{ 14 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-5x+6)& = & 1 \color{red}{-} (-12+x) \\\Leftrightarrow & -20x+24& = &1+12-x \\\Leftrightarrow & -20x \color{red}{+24} & = &13 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -20x+x& = &13-24 \\\Leftrightarrow & -19x& = &-11 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-11}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{11}{19} & & \\ & V = \left\{ \frac{11}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-5x-3)& = & -13 \color{red}{-} (-4+x) \\\Leftrightarrow & -30x-18& = &-13+4-x \\\Leftrightarrow & -30x \color{red}{-18} & = &-9 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & -30x+x& = &-9+18 \\\Leftrightarrow & -29x& = &9 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{9}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-9}{29} & & \\ & V = \left\{ \frac{-9}{29} \right\} & \\\end{align}\)