Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (6x-3)& = & -12 \color{red}{-} (-2+x) \\\Leftrightarrow & 36x-18& = &-12+2-x \\\Leftrightarrow & 36x \color{red}{-18} & = &-10 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 36x+x& = &-10+18 \\\Leftrightarrow & 37x& = &8 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{8}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{8}{37} & & \\ & V = \left\{ \frac{8}{37} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-6x+3)& = & -8 \color{red}{-} (4+x) \\\Leftrightarrow & -24x+12& = &-8-4-x \\\Leftrightarrow & -24x \color{red}{+12} & = &-12 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -24x+x& = &-12-12 \\\Leftrightarrow & -23x& = &-24 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-24}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{24}{23} & & \\ & V = \left\{ \frac{24}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-4x-5)& = & 10 \color{red}{+} (-7+x) \\\Leftrightarrow & -20x-25& = &10-7+x \\\Leftrightarrow & -20x \color{red}{-25} & = &3 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-25} \color{blue}{+25} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{+25} \\\Leftrightarrow & -20x-x& = &3+25 \\\Leftrightarrow & -21x& = &28 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{28}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-4}{3} & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (4x-1)& = & 11 \color{red}{-} (3+x) \\\Leftrightarrow & 20x-5& = &11-3-x \\\Leftrightarrow & 20x \color{red}{-5} & = &8 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-5} \color{blue}{+5} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{+5} \\\Leftrightarrow & 20x+x& = &8+5 \\\Leftrightarrow & 21x& = &13 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{13}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{13}{21} & & \\ & V = \left\{ \frac{13}{21} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-4x+1)& = & 2 \color{red}{+} (6+x) \\\Leftrightarrow & -12x+3& = &2+6+x \\\Leftrightarrow & -12x \color{red}{+3} & = &8 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & -12x-x& = &8-3 \\\Leftrightarrow & -13x& = &5 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{5}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-5}{13} & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-x+1)& = & 9 \color{red}{+} (5-5x) \\\Leftrightarrow & -6x+6& = &9+5-5x \\\Leftrightarrow & -6x \color{red}{+6} & = &14 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &14 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & -6x+5x& = &14-6 \\\Leftrightarrow & -x& = &8 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{8}{ \color{red}{-1} } \\\Leftrightarrow & x = -8 & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (5x+7)& = & -7 \color{red}{+} (3+x) \\\Leftrightarrow & 30x+42& = &-7+3+x \\\Leftrightarrow & 30x \color{red}{+42} & = &-4 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & 30x-x& = &-4-42 \\\Leftrightarrow & 29x& = &-46 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-46}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-46}{29} & & \\ & V = \left\{ \frac{-46}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (x-1)& = & -4 \color{red}{-} (10-5x) \\\Leftrightarrow & 3x-3& = &-4-10+5x \\\Leftrightarrow & 3x \color{red}{-3} & = &-14 \color{red}{+5x} \\\Leftrightarrow & 3x \color{red}{-3} \color{blue}{+3} \color{blue}{-5x} & = &-14 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+3} \\\Leftrightarrow & 3x-5x& = &-14+3 \\\Leftrightarrow & -2x& = &-11 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{-11}{ \color{red}{-2} } \\\Leftrightarrow & x = \frac{11}{2} & & \\ & V = \left\{ \frac{11}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-3x-2)& = & -14 \color{red}{+} (12-4x) \\\Leftrightarrow & -9x-6& = &-14+12-4x \\\Leftrightarrow & -9x \color{red}{-6} & = &-2 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{-6} \color{blue}{+6} \color{blue}{+4x} & = &-2 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+6} \\\Leftrightarrow & -9x+4x& = &-2+6 \\\Leftrightarrow & -5x& = &4 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{4}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-4}{5} & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-6x+1)& = & -10 \color{red}{-} (-3+x) \\\Leftrightarrow & -12x+2& = &-10+3-x \\\Leftrightarrow & -12x \color{red}{+2} & = &-7 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+2} \color{blue}{-2} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{-2} \\\Leftrightarrow & -12x+x& = &-7-2 \\\Leftrightarrow & -11x& = &-9 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-9}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{9}{11} & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-5x+7)& = & -2 \color{red}{-} (11+x) \\\Leftrightarrow & -20x+28& = &-2-11-x \\\Leftrightarrow & -20x \color{red}{+28} & = &-13 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & -20x+x& = &-13-28 \\\Leftrightarrow & -19x& = &-41 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-41}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{41}{19} & & \\ & V = \left\{ \frac{41}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (2x+1)& = & -14 \color{red}{-} (2+x) \\\Leftrightarrow & 10x+5& = &-14-2-x \\\Leftrightarrow & 10x \color{red}{+5} & = &-16 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{+5} \color{blue}{-5} \color{blue}{+x} & = &-16 \color{red}{-x} \color{blue}{+x} \color{blue}{-5} \\\Leftrightarrow & 10x+x& = &-16-5 \\\Leftrightarrow & 11x& = &-21 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-21}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-21}{11} & & \\ & V = \left\{ \frac{-21}{11} \right\} & \\\end{align}\)