Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (2x+5)& = & 9 \color{red}{-} (-4+x) \\\Leftrightarrow & 8x+20& = &9+4-x \\\Leftrightarrow & 8x \color{red}{+20} & = &13 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 8x+x& = &13-20 \\\Leftrightarrow & 9x& = &-7 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-7}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-7}{9} & & \\ & V = \left\{ \frac{-7}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-2x-3)& = & -15 \color{red}{+} (-13+x) \\\Leftrightarrow & -10x-15& = &-15-13+x \\\Leftrightarrow & -10x \color{red}{-15} & = &-28 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &-28 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & -10x-x& = &-28+15 \\\Leftrightarrow & -11x& = &-13 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-13}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{13}{11} & & \\ & V = \left\{ \frac{13}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (4x+1)& = & 7 \color{red}{+} (-7-3x) \\\Leftrightarrow & 16x+4& = &7-7-3x \\\Leftrightarrow & 16x \color{red}{+4} & = &0 \color{red}{-3x} \\\Leftrightarrow & 16x \color{red}{+4} \color{blue}{-4} \color{blue}{+3x} & = &0 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-4} \\\Leftrightarrow & 16x+3x& = &0-4 \\\Leftrightarrow & 19x& = &-4 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-4}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-4}{19} & & \\ & V = \left\{ \frac{-4}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (x+1)& = & -6 \color{red}{+} (-2-5x) \\\Leftrightarrow & 6x+6& = &-6-2-5x \\\Leftrightarrow & 6x \color{red}{+6} & = &-8 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &-8 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & 6x+5x& = &-8-6 \\\Leftrightarrow & 11x& = &-14 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-14}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-14}{11} & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (2x-3)& = & -1 \color{red}{-} (9+x) \\\Leftrightarrow & 12x-18& = &-1-9-x \\\Leftrightarrow & 12x \color{red}{-18} & = &-10 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 12x+x& = &-10+18 \\\Leftrightarrow & 13x& = &8 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{8}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{8}{13} & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-3x-4)& = & -14 \color{red}{+} (-1-5x) \\\Leftrightarrow & -18x-24& = &-14-1-5x \\\Leftrightarrow & -18x \color{red}{-24} & = &-15 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-24} \color{blue}{+24} \color{blue}{+5x} & = &-15 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+24} \\\Leftrightarrow & -18x+5x& = &-15+24 \\\Leftrightarrow & -13x& = &9 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{9}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-9}{13} & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-4x-7)& = & -4 \color{red}{-} (-10+x) \\\Leftrightarrow & -24x-42& = &-4+10-x \\\Leftrightarrow & -24x \color{red}{-42} & = &6 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & -24x+x& = &6+42 \\\Leftrightarrow & -23x& = &48 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{48}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-48}{23} & & \\ & V = \left\{ \frac{-48}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (6x+3)& = & -9 \color{red}{-} (9-5x) \\\Leftrightarrow & 18x+9& = &-9-9+5x \\\Leftrightarrow & 18x \color{red}{+9} & = &-18 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{+9} \color{blue}{-9} \color{blue}{-5x} & = &-18 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-9} \\\Leftrightarrow & 18x-5x& = &-18-9 \\\Leftrightarrow & 13x& = &-27 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-27}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-27}{13} & & \\ & V = \left\{ \frac{-27}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-x-4)& = & -9 \color{red}{-} (10+x) \\\Leftrightarrow & -4x-16& = &-9-10-x \\\Leftrightarrow & -4x \color{red}{-16} & = &-19 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & -4x+x& = &-19+16 \\\Leftrightarrow & -3x& = &-3 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-3}{ \color{red}{-3} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (3x+7)& = & 10 \color{red}{-} (14+x) \\\Leftrightarrow & 12x+28& = &10-14-x \\\Leftrightarrow & 12x \color{red}{+28} & = &-4 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & 12x+x& = &-4-28 \\\Leftrightarrow & 13x& = &-32 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-32}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-32}{13} & & \\ & V = \left\{ \frac{-32}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-3x-1)& = & -4 \color{red}{+} (-4+x) \\\Leftrightarrow & -6x-2& = &-4-4+x \\\Leftrightarrow & -6x \color{red}{-2} & = &-8 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & -6x-x& = &-8+2 \\\Leftrightarrow & -7x& = &-6 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-6}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{6}{7} & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-6x-1)& = & 3 \color{red}{+} (-9+x) \\\Leftrightarrow & -30x-5& = &3-9+x \\\Leftrightarrow & -30x \color{red}{-5} & = &-6 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-5} \color{blue}{+5} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+5} \\\Leftrightarrow & -30x-x& = &-6+5 \\\Leftrightarrow & -31x& = &-1 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-1}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{1}{31} & & \\ & V = \left\{ \frac{1}{31} \right\} & \\\end{align}\)