Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-5x-1)& = & -14 \color{red}{-} (15-2x) \\\Leftrightarrow & -25x-5& = &-14-15+2x \\\Leftrightarrow & -25x \color{red}{-5} & = &-29 \color{red}{+2x} \\\Leftrightarrow & -25x \color{red}{-5} \color{blue}{+5} \color{blue}{-2x} & = &-29 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+5} \\\Leftrightarrow & -25x-2x& = &-29+5 \\\Leftrightarrow & -27x& = &-24 \\\Leftrightarrow & \frac{-27x}{ \color{red}{-27} }& = &\frac{-24}{ \color{red}{-27} } \\\Leftrightarrow & x = \frac{8}{9} & & \\ & V = \left\{ \frac{8}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (5x+7)& = & 5 \color{red}{+} (1+x) \\\Leftrightarrow & 20x+28& = &5+1+x \\\Leftrightarrow & 20x \color{red}{+28} & = &6 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & 20x-x& = &6-28 \\\Leftrightarrow & 19x& = &-22 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-22}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-22}{19} & & \\ & V = \left\{ \frac{-22}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (x-5)& = & -1 \color{red}{+} (10+3x) \\\Leftrightarrow & 4x-20& = &-1+10+3x \\\Leftrightarrow & 4x \color{red}{-20} & = &9 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-20} \color{blue}{+20} \color{blue}{-3x} & = &9 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+20} \\\Leftrightarrow & 4x-3x& = &9+20 \\\Leftrightarrow & x& = &29 \\ & V = \left\{ 29 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-6x+6)& = & -7 \color{red}{-} (1+x) \\\Leftrightarrow & -24x+24& = &-7-1-x \\\Leftrightarrow & -24x \color{red}{+24} & = &-8 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -24x+x& = &-8-24 \\\Leftrightarrow & -23x& = &-32 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-32}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{32}{23} & & \\ & V = \left\{ \frac{32}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (x-2)& = & -8 \color{red}{+} (8-5x) \\\Leftrightarrow & 3x-6& = &-8+8-5x \\\Leftrightarrow & 3x \color{red}{-6} & = &0 \color{red}{-5x} \\\Leftrightarrow & 3x \color{red}{-6} \color{blue}{+6} \color{blue}{+5x} & = &0 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+6} \\\Leftrightarrow & 3x+5x& = &0+6 \\\Leftrightarrow & 8x& = &6 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{6}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{3}{4} & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (x-4)& = & 4 \color{red}{+} (6-3x) \\\Leftrightarrow & 4x-16& = &4+6-3x \\\Leftrightarrow & 4x \color{red}{-16} & = &10 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-16} \color{blue}{+16} \color{blue}{+3x} & = &10 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+16} \\\Leftrightarrow & 4x+3x& = &10+16 \\\Leftrightarrow & 7x& = &26 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{26}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{26}{7} & & \\ & V = \left\{ \frac{26}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-3x-4)& = & -4 \color{red}{+} (-14+4x) \\\Leftrightarrow & -15x-20& = &-4-14+4x \\\Leftrightarrow & -15x \color{red}{-20} & = &-18 \color{red}{+4x} \\\Leftrightarrow & -15x \color{red}{-20} \color{blue}{+20} \color{blue}{-4x} & = &-18 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+20} \\\Leftrightarrow & -15x-4x& = &-18+20 \\\Leftrightarrow & -19x& = &2 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{2}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-2}{19} & & \\ & V = \left\{ \frac{-2}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-3x-5)& = & -8 \color{red}{+} (5+x) \\\Leftrightarrow & -12x-20& = &-8+5+x \\\Leftrightarrow & -12x \color{red}{-20} & = &-3 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & -12x-x& = &-3+20 \\\Leftrightarrow & -13x& = &17 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{17}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-17}{13} & & \\ & V = \left\{ \frac{-17}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-3x+6)& = & -7 \color{red}{-} (11+x) \\\Leftrightarrow & -18x+36& = &-7-11-x \\\Leftrightarrow & -18x \color{red}{+36} & = &-18 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &-18 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & -18x+x& = &-18-36 \\\Leftrightarrow & -17x& = &-54 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-54}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{54}{17} & & \\ & V = \left\{ \frac{54}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (5x-5)& = & -1 \color{red}{+} (-2+x) \\\Leftrightarrow & 20x-20& = &-1-2+x \\\Leftrightarrow & 20x \color{red}{-20} & = &-3 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & 20x-x& = &-3+20 \\\Leftrightarrow & 19x& = &17 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{17}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{17}{19} & & \\ & V = \left\{ \frac{17}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-3x+4)& = & 2 \color{red}{-} (5-2x) \\\Leftrightarrow & -15x+20& = &2-5+2x \\\Leftrightarrow & -15x \color{red}{+20} & = &-3 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+20} \color{blue}{-20} \color{blue}{-2x} & = &-3 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-20} \\\Leftrightarrow & -15x-2x& = &-3-20 \\\Leftrightarrow & -17x& = &-23 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-23}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{23}{17} & & \\ & V = \left\{ \frac{23}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (2x+7)& = & 11 \color{red}{+} (14+3x) \\\Leftrightarrow & 10x+35& = &11+14+3x \\\Leftrightarrow & 10x \color{red}{+35} & = &25 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+35} \color{blue}{-35} \color{blue}{-3x} & = &25 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-35} \\\Leftrightarrow & 10x-3x& = &25-35 \\\Leftrightarrow & 7x& = &-10 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-10}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-10}{7} & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)