Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-4x+5)& = & 11 \color{red}{+} (1-5x) \\\Leftrightarrow & -16x+20& = &11+1-5x \\\Leftrightarrow & -16x \color{red}{+20} & = &12 \color{red}{-5x} \\\Leftrightarrow & -16x \color{red}{+20} \color{blue}{-20} \color{blue}{+5x} & = &12 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-20} \\\Leftrightarrow & -16x+5x& = &12-20 \\\Leftrightarrow & -11x& = &-8 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-8}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{8}{11} & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-2x+1)& = & 1 \color{red}{-} (-9-5x) \\\Leftrightarrow & -6x+3& = &1+9+5x \\\Leftrightarrow & -6x \color{red}{+3} & = &10 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+3} \color{blue}{-3} \color{blue}{-5x} & = &10 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-3} \\\Leftrightarrow & -6x-5x& = &10-3 \\\Leftrightarrow & -11x& = &7 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{7}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-7}{11} & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (2x-1)& = & 7 \color{red}{+} (8+x) \\\Leftrightarrow & 6x-3& = &7+8+x \\\Leftrightarrow & 6x \color{red}{-3} & = &15 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-3} \color{blue}{+3} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{+3} \\\Leftrightarrow & 6x-x& = &15+3 \\\Leftrightarrow & 5x& = &18 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{18}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{18}{5} & & \\ & V = \left\{ \frac{18}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-5x-6)& = & 6 \color{red}{+} (10+x) \\\Leftrightarrow & -20x-24& = &6+10+x \\\Leftrightarrow & -20x \color{red}{-24} & = &16 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -20x-x& = &16+24 \\\Leftrightarrow & -21x& = &40 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{40}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-40}{21} & & \\ & V = \left\{ \frac{-40}{21} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-4x+3)& = & -10 \color{red}{-} (5+x) \\\Leftrightarrow & -24x+18& = &-10-5-x \\\Leftrightarrow & -24x \color{red}{+18} & = &-15 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &-15 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -24x+x& = &-15-18 \\\Leftrightarrow & -23x& = &-33 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-33}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{33}{23} & & \\ & V = \left\{ \frac{33}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-2x+7)& = & -15 \color{red}{+} (9+x) \\\Leftrightarrow & -6x+21& = &-15+9+x \\\Leftrightarrow & -6x \color{red}{+21} & = &-6 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+21} \color{blue}{-21} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-21} \\\Leftrightarrow & -6x-x& = &-6-21 \\\Leftrightarrow & -7x& = &-27 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-27}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{27}{7} & & \\ & V = \left\{ \frac{27}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-x+4)& = & -10 \color{red}{+} (10+3x) \\\Leftrightarrow & -2x+8& = &-10+10+3x \\\Leftrightarrow & -2x \color{red}{+8} & = &0 \color{red}{+3x} \\\Leftrightarrow & -2x \color{red}{+8} \color{blue}{-8} \color{blue}{-3x} & = &0 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-8} \\\Leftrightarrow & -2x-3x& = &0-8 \\\Leftrightarrow & -5x& = &-8 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-8}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{8}{5} & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (5x-7)& = & -8 \color{red}{-} (-6+3x) \\\Leftrightarrow & 10x-14& = &-8+6-3x \\\Leftrightarrow & 10x \color{red}{-14} & = &-2 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-14} \color{blue}{+14} \color{blue}{+3x} & = &-2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+14} \\\Leftrightarrow & 10x+3x& = &-2+14 \\\Leftrightarrow & 13x& = &12 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{12}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{12}{13} & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-4x-7)& = & -13 \color{red}{-} (8+x) \\\Leftrightarrow & -20x-35& = &-13-8-x \\\Leftrightarrow & -20x \color{red}{-35} & = &-21 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-35} \color{blue}{+35} \color{blue}{+x} & = &-21 \color{red}{-x} \color{blue}{+x} \color{blue}{+35} \\\Leftrightarrow & -20x+x& = &-21+35 \\\Leftrightarrow & -19x& = &14 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{14}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-14}{19} & & \\ & V = \left\{ \frac{-14}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-5x+3)& = & -8 \color{red}{-} (14-3x) \\\Leftrightarrow & -10x+6& = &-8-14+3x \\\Leftrightarrow & -10x \color{red}{+6} & = &-22 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+6} \color{blue}{-6} \color{blue}{-3x} & = &-22 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-6} \\\Leftrightarrow & -10x-3x& = &-22-6 \\\Leftrightarrow & -13x& = &-28 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-28}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{28}{13} & & \\ & V = \left\{ \frac{28}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-x+2)& = & -10 \color{red}{-} (15+x) \\\Leftrightarrow & -6x+12& = &-10-15-x \\\Leftrightarrow & -6x \color{red}{+12} & = &-25 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-25 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -6x+x& = &-25-12 \\\Leftrightarrow & -5x& = &-37 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-37}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{37}{5} & & \\ & V = \left\{ \frac{37}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-x-2)& = & -9 \color{red}{+} (-7+3x) \\\Leftrightarrow & -4x-8& = &-9-7+3x \\\Leftrightarrow & -4x \color{red}{-8} & = &-16 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-8} \color{blue}{+8} \color{blue}{-3x} & = &-16 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+8} \\\Leftrightarrow & -4x-3x& = &-16+8 \\\Leftrightarrow & -7x& = &-8 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-8}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{8}{7} & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)