Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (5x+4)& = & 12 \color{red}{-} (-13+x) \\\Leftrightarrow & 20x+16& = &12+13-x \\\Leftrightarrow & 20x \color{red}{+16} & = &25 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &25 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & 20x+x& = &25-16 \\\Leftrightarrow & 21x& = &9 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{9}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{3}{7} & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-3x+5)& = & -11 \color{red}{-} (-15+5x) \\\Leftrightarrow & -12x+20& = &-11+15-5x \\\Leftrightarrow & -12x \color{red}{+20} & = &4 \color{red}{-5x} \\\Leftrightarrow & -12x \color{red}{+20} \color{blue}{-20} \color{blue}{+5x} & = &4 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-20} \\\Leftrightarrow & -12x+5x& = &4-20 \\\Leftrightarrow & -7x& = &-16 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-16}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{16}{7} & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-x+7)& = & 5 \color{red}{+} (11+2x) \\\Leftrightarrow & -5x+35& = &5+11+2x \\\Leftrightarrow & -5x \color{red}{+35} & = &16 \color{red}{+2x} \\\Leftrightarrow & -5x \color{red}{+35} \color{blue}{-35} \color{blue}{-2x} & = &16 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-35} \\\Leftrightarrow & -5x-2x& = &16-35 \\\Leftrightarrow & -7x& = &-19 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-19}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{19}{7} & & \\ & V = \left\{ \frac{19}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (x-1)& = & 8 \color{red}{+} (-14+x) \\\Leftrightarrow & 6x-6& = &8-14+x \\\Leftrightarrow & 6x \color{red}{-6} & = &-6 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 6x-x& = &-6+6 \\\Leftrightarrow & 5x& = &0 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{0}{ \color{red}{5} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-4x+4)& = & -9 \color{red}{+} (14+5x) \\\Leftrightarrow & -24x+24& = &-9+14+5x \\\Leftrightarrow & -24x \color{red}{+24} & = &5 \color{red}{+5x} \\\Leftrightarrow & -24x \color{red}{+24} \color{blue}{-24} \color{blue}{-5x} & = &5 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-24} \\\Leftrightarrow & -24x-5x& = &5-24 \\\Leftrightarrow & -29x& = &-19 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-19}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{19}{29} & & \\ & V = \left\{ \frac{19}{29} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (2x+4)& = & -15 \color{red}{+} (2+11x) \\\Leftrightarrow & 12x+24& = &-15+2+11x \\\Leftrightarrow & 12x \color{red}{+24} & = &-13 \color{red}{+11x} \\\Leftrightarrow & 12x \color{red}{+24} \color{blue}{-24} \color{blue}{-11x} & = &-13 \color{red}{+11x} \color{blue}{-11x} \color{blue}{-24} \\\Leftrightarrow & 12x-11x& = &-13-24 \\\Leftrightarrow & x& = &-37 \\ & V = \left\{ -37 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (6x-5)& = & 4 \color{red}{-} (-2+11x) \\\Leftrightarrow & 12x-10& = &4+2-11x \\\Leftrightarrow & 12x \color{red}{-10} & = &6 \color{red}{-11x} \\\Leftrightarrow & 12x \color{red}{-10} \color{blue}{+10} \color{blue}{+11x} & = &6 \color{red}{-11x} \color{blue}{+11x} \color{blue}{+10} \\\Leftrightarrow & 12x+11x& = &6+10 \\\Leftrightarrow & 23x& = &16 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{16}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{16}{23} & & \\ & V = \left\{ \frac{16}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (4x-5)& = & -3 \color{red}{-} (9+x) \\\Leftrightarrow & 8x-10& = &-3-9-x \\\Leftrightarrow & 8x \color{red}{-10} & = &-12 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 8x+x& = &-12+10 \\\Leftrightarrow & 9x& = &-2 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-2}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-2}{9} & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (2x+5)& = & 3 \color{red}{-} (-6+3x) \\\Leftrightarrow & 10x+25& = &3+6-3x \\\Leftrightarrow & 10x \color{red}{+25} & = &9 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+25} \color{blue}{-25} \color{blue}{+3x} & = &9 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-25} \\\Leftrightarrow & 10x+3x& = &9-25 \\\Leftrightarrow & 13x& = &-16 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-16}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-16}{13} & & \\ & V = \left\{ \frac{-16}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-6x-1)& = & -14 \color{red}{+} (1-5x) \\\Leftrightarrow & -18x-3& = &-14+1-5x \\\Leftrightarrow & -18x \color{red}{-3} & = &-13 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-3} \color{blue}{+3} \color{blue}{+5x} & = &-13 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+3} \\\Leftrightarrow & -18x+5x& = &-13+3 \\\Leftrightarrow & -13x& = &-10 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-10}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{10}{13} & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-3x+7)& = & 5 \color{red}{-} (-11+5x) \\\Leftrightarrow & -18x+42& = &5+11-5x \\\Leftrightarrow & -18x \color{red}{+42} & = &16 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{+42} \color{blue}{-42} \color{blue}{+5x} & = &16 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-42} \\\Leftrightarrow & -18x+5x& = &16-42 \\\Leftrightarrow & -13x& = &-26 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-26}{ \color{red}{-13} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (6x-6)& = & 4 \color{red}{+} (-2+5x) \\\Leftrightarrow & 24x-24& = &4-2+5x \\\Leftrightarrow & 24x \color{red}{-24} & = &2 \color{red}{+5x} \\\Leftrightarrow & 24x \color{red}{-24} \color{blue}{+24} \color{blue}{-5x} & = &2 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+24} \\\Leftrightarrow & 24x-5x& = &2+24 \\\Leftrightarrow & 19x& = &26 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{26}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{26}{19} & & \\ & V = \left\{ \frac{26}{19} \right\} & \\\end{align}\)