Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-3x+1)& = & -8 \color{red}{-} (10+2x) \\\Leftrightarrow & -15x+5& = &-8-10-2x \\\Leftrightarrow & -15x \color{red}{+5} & = &-18 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+5} \color{blue}{-5} \color{blue}{+2x} & = &-18 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-5} \\\Leftrightarrow & -15x+2x& = &-18-5 \\\Leftrightarrow & -13x& = &-23 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-23}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{23}{13} & & \\ & V = \left\{ \frac{23}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-3x-5)& = & -6 \color{red}{-} (11+2x) \\\Leftrightarrow & -15x-25& = &-6-11-2x \\\Leftrightarrow & -15x \color{red}{-25} & = &-17 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{-25} \color{blue}{+25} \color{blue}{+2x} & = &-17 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+25} \\\Leftrightarrow & -15x+2x& = &-17+25 \\\Leftrightarrow & -13x& = &8 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{8}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-8}{13} & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-3x-3)& = & -1 \color{red}{+} (10+x) \\\Leftrightarrow & -15x-15& = &-1+10+x \\\Leftrightarrow & -15x \color{red}{-15} & = &9 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & -15x-x& = &9+15 \\\Leftrightarrow & -16x& = &24 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{24}{ \color{red}{-16} } \\\Leftrightarrow & x = \frac{-3}{2} & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-3x+6)& = & 14 \color{red}{-} (7-5x) \\\Leftrightarrow & -18x+36& = &14-7+5x \\\Leftrightarrow & -18x \color{red}{+36} & = &7 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{+36} \color{blue}{-36} \color{blue}{-5x} & = &7 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-36} \\\Leftrightarrow & -18x-5x& = &7-36 \\\Leftrightarrow & -23x& = &-29 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-29}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{29}{23} & & \\ & V = \left\{ \frac{29}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (2x-2)& = & 13 \color{red}{-} (10+x) \\\Leftrightarrow & 4x-4& = &13-10-x \\\Leftrightarrow & 4x \color{red}{-4} & = &3 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 4x+x& = &3+4 \\\Leftrightarrow & 5x& = &7 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{7}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{7}{5} & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (5x-2)& = & 14 \color{red}{-} (-4+x) \\\Leftrightarrow & 25x-10& = &14+4-x \\\Leftrightarrow & 25x \color{red}{-10} & = &18 \color{red}{-x} \\\Leftrightarrow & 25x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &18 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 25x+x& = &18+10 \\\Leftrightarrow & 26x& = &28 \\\Leftrightarrow & \frac{26x}{ \color{red}{26} }& = &\frac{28}{ \color{red}{26} } \\\Leftrightarrow & x = \frac{14}{13} & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (2x+7)& = & -3 \color{red}{+} (-8+x) \\\Leftrightarrow & 6x+21& = &-3-8+x \\\Leftrightarrow & 6x \color{red}{+21} & = &-11 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+21} \color{blue}{-21} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{-21} \\\Leftrightarrow & 6x-x& = &-11-21 \\\Leftrightarrow & 5x& = &-32 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-32}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-32}{5} & & \\ & V = \left\{ \frac{-32}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-3x-2)& = & 12 \color{red}{+} (6+x) \\\Leftrightarrow & -12x-8& = &12+6+x \\\Leftrightarrow & -12x \color{red}{-8} & = &18 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &18 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -12x-x& = &18+8 \\\Leftrightarrow & -13x& = &26 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{26}{ \color{red}{-13} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (5x+6)& = & -13 \color{red}{-} (-13-2x) \\\Leftrightarrow & 15x+18& = &-13+13+2x \\\Leftrightarrow & 15x \color{red}{+18} & = &0 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+18} \color{blue}{-18} \color{blue}{-2x} & = &0 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-18} \\\Leftrightarrow & 15x-2x& = &0-18 \\\Leftrightarrow & 13x& = &-18 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-18}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-18}{13} & & \\ & V = \left\{ \frac{-18}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-4x+5)& = & 7 \color{red}{-} (-10+x) \\\Leftrightarrow & -24x+30& = &7+10-x \\\Leftrightarrow & -24x \color{red}{+30} & = &17 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & -24x+x& = &17-30 \\\Leftrightarrow & -23x& = &-13 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-13}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{13}{23} & & \\ & V = \left\{ \frac{13}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-5x+7)& = & 1 \color{red}{-} (-4+x) \\\Leftrightarrow & -30x+42& = &1+4-x \\\Leftrightarrow & -30x \color{red}{+42} & = &5 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & -30x+x& = &5-42 \\\Leftrightarrow & -29x& = &-37 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-37}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{37}{29} & & \\ & V = \left\{ \frac{37}{29} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-4x-2)& = & -9 \color{red}{+} (-3+x) \\\Leftrightarrow & -12x-6& = &-9-3+x \\\Leftrightarrow & -12x \color{red}{-6} & = &-12 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -12x-x& = &-12+6 \\\Leftrightarrow & -13x& = &-6 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-6}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{6}{13} & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)