Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-2x+2)& = & 8 \color{red}{-} (7-5x) \\\Leftrightarrow & -8x+8& = &8-7+5x \\\Leftrightarrow & -8x \color{red}{+8} & = &1 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{+8} \color{blue}{-8} \color{blue}{-5x} & = &1 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-8} \\\Leftrightarrow & -8x-5x& = &1-8 \\\Leftrightarrow & -13x& = &-7 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-7}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{7}{13} & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (4x-5)& = & -9 \color{red}{+} (5+x) \\\Leftrightarrow & 24x-30& = &-9+5+x \\\Leftrightarrow & 24x \color{red}{-30} & = &-4 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 24x-x& = &-4+30 \\\Leftrightarrow & 23x& = &26 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{26}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{26}{23} & & \\ & V = \left\{ \frac{26}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (x-1)& = & -8 \color{red}{-} (-11+x) \\\Leftrightarrow & 5x-5& = &-8+11-x \\\Leftrightarrow & 5x \color{red}{-5} & = &3 \color{red}{-x} \\\Leftrightarrow & 5x \color{red}{-5} \color{blue}{+5} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{+5} \\\Leftrightarrow & 5x+x& = &3+5 \\\Leftrightarrow & 6x& = &8 \\\Leftrightarrow & \frac{6x}{ \color{red}{6} }& = &\frac{8}{ \color{red}{6} } \\\Leftrightarrow & x = \frac{4}{3} & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-3x-3)& = & 12 \color{red}{+} (13+x) \\\Leftrightarrow & -12x-12& = &12+13+x \\\Leftrightarrow & -12x \color{red}{-12} & = &25 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &25 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -12x-x& = &25+12 \\\Leftrightarrow & -13x& = &37 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{37}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-37}{13} & & \\ & V = \left\{ \frac{-37}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (x+1)& = & 6 \color{red}{-} (1-5x) \\\Leftrightarrow & 6x+6& = &6-1+5x \\\Leftrightarrow & 6x \color{red}{+6} & = &5 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+6} \color{blue}{-6} \color{blue}{-5x} & = &5 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-6} \\\Leftrightarrow & 6x-5x& = &5-6 \\\Leftrightarrow & x& = &-1 \\ & V = \left\{ -1 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-x-2)& = & 9 \color{red}{+} (-2+x) \\\Leftrightarrow & -5x-10& = &9-2+x \\\Leftrightarrow & -5x \color{red}{-10} & = &7 \color{red}{+x} \\\Leftrightarrow & -5x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & -5x-x& = &7+10 \\\Leftrightarrow & -6x& = &17 \\\Leftrightarrow & \frac{-6x}{ \color{red}{-6} }& = &\frac{17}{ \color{red}{-6} } \\\Leftrightarrow & x = \frac{-17}{6} & & \\ & V = \left\{ \frac{-17}{6} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (4x-6)& = & -14 \color{red}{-} (5-3x) \\\Leftrightarrow & 16x-24& = &-14-5+3x \\\Leftrightarrow & 16x \color{red}{-24} & = &-19 \color{red}{+3x} \\\Leftrightarrow & 16x \color{red}{-24} \color{blue}{+24} \color{blue}{-3x} & = &-19 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+24} \\\Leftrightarrow & 16x-3x& = &-19+24 \\\Leftrightarrow & 13x& = &5 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{5}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{5}{13} & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (4x-4)& = & 14 \color{red}{-} (7+x) \\\Leftrightarrow & 20x-20& = &14-7-x \\\Leftrightarrow & 20x \color{red}{-20} & = &7 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & 20x+x& = &7+20 \\\Leftrightarrow & 21x& = &27 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{27}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{9}{7} & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (4x+6)& = & 14 \color{red}{+} (-10+x) \\\Leftrightarrow & 12x+18& = &14-10+x \\\Leftrightarrow & 12x \color{red}{+18} & = &4 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & 12x-x& = &4-18 \\\Leftrightarrow & 11x& = &-14 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-14}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-14}{11} & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-5x-7)& = & 8 \color{red}{+} (-2+x) \\\Leftrightarrow & -20x-28& = &8-2+x \\\Leftrightarrow & -20x \color{red}{-28} & = &6 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & -20x-x& = &6+28 \\\Leftrightarrow & -21x& = &34 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{34}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-34}{21} & & \\ & V = \left\{ \frac{-34}{21} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (x-5)& = & -1 \color{red}{-} (-6+x) \\\Leftrightarrow & 2x-10& = &-1+6-x \\\Leftrightarrow & 2x \color{red}{-10} & = &5 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 2x+x& = &5+10 \\\Leftrightarrow & 3x& = &15 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{15}{ \color{red}{3} } \\\Leftrightarrow & x = 5 & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-4x+7)& = & -5 \color{red}{+} (5-5x) \\\Leftrightarrow & -16x+28& = &-5+5-5x \\\Leftrightarrow & -16x \color{red}{+28} & = &0 \color{red}{-5x} \\\Leftrightarrow & -16x \color{red}{+28} \color{blue}{-28} \color{blue}{+5x} & = &0 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-28} \\\Leftrightarrow & -16x+5x& = &0-28 \\\Leftrightarrow & -11x& = &-28 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-28}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{28}{11} & & \\ & V = \left\{ \frac{28}{11} \right\} & \\\end{align}\)