Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (2x-7)& = & -1 \color{red}{-} (-13+x) \\\Leftrightarrow & 6x-21& = &-1+13-x \\\Leftrightarrow & 6x \color{red}{-21} & = &12 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-21} \color{blue}{+21} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{+21} \\\Leftrightarrow & 6x+x& = &12+21 \\\Leftrightarrow & 7x& = &33 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{33}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{33}{7} & & \\ & V = \left\{ \frac{33}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (5x+5)& = & -8 \color{red}{+} (-6+x) \\\Leftrightarrow & 10x+10& = &-8-6+x \\\Leftrightarrow & 10x \color{red}{+10} & = &-14 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & 10x-x& = &-14-10 \\\Leftrightarrow & 9x& = &-24 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-24}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-8}{3} & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-5x+1)& = & -11 \color{red}{+} (-10+x) \\\Leftrightarrow & -30x+6& = &-11-10+x \\\Leftrightarrow & -30x \color{red}{+6} & = &-21 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-21 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -30x-x& = &-21-6 \\\Leftrightarrow & -31x& = &-27 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-27}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{27}{31} & & \\ & V = \left\{ \frac{27}{31} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (2x+7)& = & 15 \color{red}{+} (4-3x) \\\Leftrightarrow & 4x+14& = &15+4-3x \\\Leftrightarrow & 4x \color{red}{+14} & = &19 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+14} \color{blue}{-14} \color{blue}{+3x} & = &19 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-14} \\\Leftrightarrow & 4x+3x& = &19-14 \\\Leftrightarrow & 7x& = &5 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{5}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{5}{7} & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-5x+3)& = & 10 \color{red}{-} (-4+x) \\\Leftrightarrow & -10x+6& = &10+4-x \\\Leftrightarrow & -10x \color{red}{+6} & = &14 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -10x+x& = &14-6 \\\Leftrightarrow & -9x& = &8 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{8}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-8}{9} & & \\ & V = \left\{ \frac{-8}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (x-4)& = & 8 \color{red}{+} (-3-5x) \\\Leftrightarrow & 3x-12& = &8-3-5x \\\Leftrightarrow & 3x \color{red}{-12} & = &5 \color{red}{-5x} \\\Leftrightarrow & 3x \color{red}{-12} \color{blue}{+12} \color{blue}{+5x} & = &5 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+12} \\\Leftrightarrow & 3x+5x& = &5+12 \\\Leftrightarrow & 8x& = &17 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{17}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{17}{8} & & \\ & V = \left\{ \frac{17}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (x-3)& = & 5 \color{red}{-} (-3+x) \\\Leftrightarrow & 3x-9& = &5+3-x \\\Leftrightarrow & 3x \color{red}{-9} & = &8 \color{red}{-x} \\\Leftrightarrow & 3x \color{red}{-9} \color{blue}{+9} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{+9} \\\Leftrightarrow & 3x+x& = &8+9 \\\Leftrightarrow & 4x& = &17 \\\Leftrightarrow & \frac{4x}{ \color{red}{4} }& = &\frac{17}{ \color{red}{4} } \\\Leftrightarrow & x = \frac{17}{4} & & \\ & V = \left\{ \frac{17}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-2x-3)& = & 7 \color{red}{-} (15+x) \\\Leftrightarrow & -4x-6& = &7-15-x \\\Leftrightarrow & -4x \color{red}{-6} & = &-8 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -4x+x& = &-8+6 \\\Leftrightarrow & -3x& = &-2 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-2}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{2}{3} & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (6x+3)& = & -11 \color{red}{-} (1+x) \\\Leftrightarrow & 36x+18& = &-11-1-x \\\Leftrightarrow & 36x \color{red}{+18} & = &-12 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 36x+x& = &-12-18 \\\Leftrightarrow & 37x& = &-30 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{-30}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{-30}{37} & & \\ & V = \left\{ \frac{-30}{37} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-5x-7)& = & -12 \color{red}{+} (14+x) \\\Leftrightarrow & -15x-21& = &-12+14+x \\\Leftrightarrow & -15x \color{red}{-21} & = &2 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{-21} \color{blue}{+21} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{+21} \\\Leftrightarrow & -15x-x& = &2+21 \\\Leftrightarrow & -16x& = &23 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{23}{ \color{red}{-16} } \\\Leftrightarrow & x = \frac{-23}{16} & & \\ & V = \left\{ \frac{-23}{16} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (5x+2)& = & -13 \color{red}{-} (13+3x) \\\Leftrightarrow & 10x+4& = &-13-13-3x \\\Leftrightarrow & 10x \color{red}{+4} & = &-26 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+4} \color{blue}{-4} \color{blue}{+3x} & = &-26 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-4} \\\Leftrightarrow & 10x+3x& = &-26-4 \\\Leftrightarrow & 13x& = &-30 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-30}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-30}{13} & & \\ & V = \left\{ \frac{-30}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-2x-2)& = & 8 \color{red}{+} (6+x) \\\Leftrightarrow & -12x-12& = &8+6+x \\\Leftrightarrow & -12x \color{red}{-12} & = &14 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -12x-x& = &14+12 \\\Leftrightarrow & -13x& = &26 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{26}{ \color{red}{-13} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)