Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-6x+7)& = & -4 \color{red}{+} (8+x) \\\Leftrightarrow & -30x+35& = &-4+8+x \\\Leftrightarrow & -30x \color{red}{+35} & = &4 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+35} \color{blue}{-35} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{-35} \\\Leftrightarrow & -30x-x& = &4-35 \\\Leftrightarrow & -31x& = &-31 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-31}{ \color{red}{-31} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (4x+5)& = & -1 \color{red}{-} (3+x) \\\Leftrightarrow & 16x+20& = &-1-3-x \\\Leftrightarrow & 16x \color{red}{+20} & = &-4 \color{red}{-x} \\\Leftrightarrow & 16x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 16x+x& = &-4-20 \\\Leftrightarrow & 17x& = &-24 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-24}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-24}{17} & & \\ & V = \left\{ \frac{-24}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (4x+6)& = & -5 \color{red}{+} (12-5x) \\\Leftrightarrow & 8x+12& = &-5+12-5x \\\Leftrightarrow & 8x \color{red}{+12} & = &7 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{+12} \color{blue}{-12} \color{blue}{+5x} & = &7 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-12} \\\Leftrightarrow & 8x+5x& = &7-12 \\\Leftrightarrow & 13x& = &-5 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-5}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-5}{13} & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-5x-5)& = & -4 \color{red}{+} (-6+x) \\\Leftrightarrow & -30x-30& = &-4-6+x \\\Leftrightarrow & -30x \color{red}{-30} & = &-10 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & -30x-x& = &-10+30 \\\Leftrightarrow & -31x& = &20 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{20}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-20}{31} & & \\ & V = \left\{ \frac{-20}{31} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (x-3)& = & -8 \color{red}{+} (2+x) \\\Leftrightarrow & 5x-15& = &-8+2+x \\\Leftrightarrow & 5x \color{red}{-15} & = &-6 \color{red}{+x} \\\Leftrightarrow & 5x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & 5x-x& = &-6+15 \\\Leftrightarrow & 4x& = &9 \\\Leftrightarrow & \frac{4x}{ \color{red}{4} }& = &\frac{9}{ \color{red}{4} } \\\Leftrightarrow & x = \frac{9}{4} & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (2x+1)& = & -7 \color{red}{+} (-10+x) \\\Leftrightarrow & 10x+5& = &-7-10+x \\\Leftrightarrow & 10x \color{red}{+5} & = &-17 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{+5} \color{blue}{-5} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{-5} \\\Leftrightarrow & 10x-x& = &-17-5 \\\Leftrightarrow & 9x& = &-22 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-22}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-22}{9} & & \\ & V = \left\{ \frac{-22}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (2x+6)& = & -2 \color{red}{+} (4-3x) \\\Leftrightarrow & 10x+30& = &-2+4-3x \\\Leftrightarrow & 10x \color{red}{+30} & = &2 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+30} \color{blue}{-30} \color{blue}{+3x} & = &2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-30} \\\Leftrightarrow & 10x+3x& = &2-30 \\\Leftrightarrow & 13x& = &-28 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-28}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-28}{13} & & \\ & V = \left\{ \frac{-28}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (5x-1)& = & -7 \color{red}{-} (14+x) \\\Leftrightarrow & 30x-6& = &-7-14-x \\\Leftrightarrow & 30x \color{red}{-6} & = &-21 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-21 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 30x+x& = &-21+6 \\\Leftrightarrow & 31x& = &-15 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-15}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-15}{31} & & \\ & V = \left\{ \frac{-15}{31} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (x-5)& = & 6 \color{red}{+} (-6-5x) \\\Leftrightarrow & 6x-30& = &6-6-5x \\\Leftrightarrow & 6x \color{red}{-30} & = &0 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-30} \color{blue}{+30} \color{blue}{+5x} & = &0 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+30} \\\Leftrightarrow & 6x+5x& = &0+30 \\\Leftrightarrow & 11x& = &30 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{30}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{30}{11} & & \\ & V = \left\{ \frac{30}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-6x-7)& = & 14 \color{red}{-} (2+x) \\\Leftrightarrow & -24x-28& = &14-2-x \\\Leftrightarrow & -24x \color{red}{-28} & = &12 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-28} \color{blue}{+28} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{+28} \\\Leftrightarrow & -24x+x& = &12+28 \\\Leftrightarrow & -23x& = &40 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{40}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-40}{23} & & \\ & V = \left\{ \frac{-40}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-6x-5)& = & -14 \color{red}{-} (-7-5x) \\\Leftrightarrow & -18x-15& = &-14+7+5x \\\Leftrightarrow & -18x \color{red}{-15} & = &-7 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{-15} \color{blue}{+15} \color{blue}{-5x} & = &-7 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+15} \\\Leftrightarrow & -18x-5x& = &-7+15 \\\Leftrightarrow & -23x& = &8 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{8}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-8}{23} & & \\ & V = \left\{ \frac{-8}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-3x+3)& = & 1 \color{red}{+} (11+4x) \\\Leftrightarrow & -15x+15& = &1+11+4x \\\Leftrightarrow & -15x \color{red}{+15} & = &12 \color{red}{+4x} \\\Leftrightarrow & -15x \color{red}{+15} \color{blue}{-15} \color{blue}{-4x} & = &12 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-15} \\\Leftrightarrow & -15x-4x& = &12-15 \\\Leftrightarrow & -19x& = &-3 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-3}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{3}{19} & & \\ & V = \left\{ \frac{3}{19} \right\} & \\\end{align}\)