Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (x-6)& = & 14 \color{red}{-} (5+3x) \\\Leftrightarrow & 2x-12& = &14-5-3x \\\Leftrightarrow & 2x \color{red}{-12} & = &9 \color{red}{-3x} \\\Leftrightarrow & 2x \color{red}{-12} \color{blue}{+12} \color{blue}{+3x} & = &9 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+12} \\\Leftrightarrow & 2x+3x& = &9+12 \\\Leftrightarrow & 5x& = &21 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{21}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{21}{5} & & \\ & V = \left\{ \frac{21}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-4x+3)& = & -10 \color{red}{+} (3+x) \\\Leftrightarrow & -8x+6& = &-10+3+x \\\Leftrightarrow & -8x \color{red}{+6} & = &-7 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -8x-x& = &-7-6 \\\Leftrightarrow & -9x& = &-13 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-13}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{13}{9} & & \\ & V = \left\{ \frac{13}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-4x-7)& = & -15 \color{red}{+} (1+x) \\\Leftrightarrow & -20x-35& = &-15+1+x \\\Leftrightarrow & -20x \color{red}{-35} & = &-14 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-35} \color{blue}{+35} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{+35} \\\Leftrightarrow & -20x-x& = &-14+35 \\\Leftrightarrow & -21x& = &21 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{21}{ \color{red}{-21} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-4x+2)& = & 1 \color{red}{+} (-14+x) \\\Leftrightarrow & -20x+10& = &1-14+x \\\Leftrightarrow & -20x \color{red}{+10} & = &-13 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & -20x-x& = &-13-10 \\\Leftrightarrow & -21x& = &-23 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-23}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{23}{21} & & \\ & V = \left\{ \frac{23}{21} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (4x-5)& = & 14 \color{red}{-} (-6+x) \\\Leftrightarrow & 16x-20& = &14+6-x \\\Leftrightarrow & 16x \color{red}{-20} & = &20 \color{red}{-x} \\\Leftrightarrow & 16x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & 16x+x& = &20+20 \\\Leftrightarrow & 17x& = &40 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{40}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{40}{17} & & \\ & V = \left\{ \frac{40}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (x-7)& = & -14 \color{red}{-} (-3+x) \\\Leftrightarrow & 6x-42& = &-14+3-x \\\Leftrightarrow & 6x \color{red}{-42} & = &-11 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & 6x+x& = &-11+42 \\\Leftrightarrow & 7x& = &31 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{31}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{31}{7} & & \\ & V = \left\{ \frac{31}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (6x-4)& = & 6 \color{red}{+} (12+x) \\\Leftrightarrow & 12x-8& = &6+12+x \\\Leftrightarrow & 12x \color{red}{-8} & = &18 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &18 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & 12x-x& = &18+8 \\\Leftrightarrow & 11x& = &26 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{26}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{26}{11} & & \\ & V = \left\{ \frac{26}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-3x-3)& = & 1 \color{red}{+} (7+x) \\\Leftrightarrow & -12x-12& = &1+7+x \\\Leftrightarrow & -12x \color{red}{-12} & = &8 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -12x-x& = &8+12 \\\Leftrightarrow & -13x& = &20 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{20}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-20}{13} & & \\ & V = \left\{ \frac{-20}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (4x-1)& = & -5 \color{red}{-} (10+x) \\\Leftrightarrow & 20x-5& = &-5-10-x \\\Leftrightarrow & 20x \color{red}{-5} & = &-15 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-5} \color{blue}{+5} \color{blue}{+x} & = &-15 \color{red}{-x} \color{blue}{+x} \color{blue}{+5} \\\Leftrightarrow & 20x+x& = &-15+5 \\\Leftrightarrow & 21x& = &-10 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-10}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-10}{21} & & \\ & V = \left\{ \frac{-10}{21} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-4x+1)& = & 15 \color{red}{+} (-13+x) \\\Leftrightarrow & -12x+3& = &15-13+x \\\Leftrightarrow & -12x \color{red}{+3} & = &2 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & -12x-x& = &2-3 \\\Leftrightarrow & -13x& = &-1 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-1}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{1}{13} & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-6x+7)& = & -9 \color{red}{-} (-10+x) \\\Leftrightarrow & -24x+28& = &-9+10-x \\\Leftrightarrow & -24x \color{red}{+28} & = &1 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & -24x+x& = &1-28 \\\Leftrightarrow & -23x& = &-27 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-27}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{27}{23} & & \\ & V = \left\{ \frac{27}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-5x-1)& = & 8 \color{red}{+} (14+x) \\\Leftrightarrow & -30x-6& = &8+14+x \\\Leftrightarrow & -30x \color{red}{-6} & = &22 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &22 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -30x-x& = &22+6 \\\Leftrightarrow & -31x& = &28 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{28}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-28}{31} & & \\ & V = \left\{ \frac{-28}{31} \right\} & \\\end{align}\)