Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-4x-3)& = & 10 \color{red}{+} (8+x) \\\Leftrightarrow & -20x-15& = &10+8+x \\\Leftrightarrow & -20x \color{red}{-15} & = &18 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &18 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & -20x-x& = &18+15 \\\Leftrightarrow & -21x& = &33 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{33}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-11}{7} & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (6x+3)& = & 5 \color{red}{-} (4+x) \\\Leftrightarrow & 30x+15& = &5-4-x \\\Leftrightarrow & 30x \color{red}{+15} & = &1 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & 30x+x& = &1-15 \\\Leftrightarrow & 31x& = &-14 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-14}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-14}{31} & & \\ & V = \left\{ \frac{-14}{31} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-2x+3)& = & 4 \color{red}{-} (11+3x) \\\Leftrightarrow & -10x+15& = &4-11-3x \\\Leftrightarrow & -10x \color{red}{+15} & = &-7 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{+15} \color{blue}{-15} \color{blue}{+3x} & = &-7 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-15} \\\Leftrightarrow & -10x+3x& = &-7-15 \\\Leftrightarrow & -7x& = &-22 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-22}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{22}{7} & & \\ & V = \left\{ \frac{22}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (6x-6)& = & -1 \color{red}{-} (11+x) \\\Leftrightarrow & 30x-30& = &-1-11-x \\\Leftrightarrow & 30x \color{red}{-30} & = &-12 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 30x+x& = &-12+30 \\\Leftrightarrow & 31x& = &18 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{18}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{18}{31} & & \\ & V = \left\{ \frac{18}{31} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-4x+3)& = & 2 \color{red}{-} (-7+x) \\\Leftrightarrow & -20x+15& = &2+7-x \\\Leftrightarrow & -20x \color{red}{+15} & = &9 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & -20x+x& = &9-15 \\\Leftrightarrow & -19x& = &-6 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-6}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{6}{19} & & \\ & V = \left\{ \frac{6}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-6x+3)& = & 13 \color{red}{-} (10+x) \\\Leftrightarrow & -24x+12& = &13-10-x \\\Leftrightarrow & -24x \color{red}{+12} & = &3 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -24x+x& = &3-12 \\\Leftrightarrow & -23x& = &-9 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-9}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{9}{23} & & \\ & V = \left\{ \frac{9}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (5x-3)& = & -2 \color{red}{-} (-1+x) \\\Leftrightarrow & 20x-12& = &-2+1-x \\\Leftrightarrow & 20x \color{red}{-12} & = &-1 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 20x+x& = &-1+12 \\\Leftrightarrow & 21x& = &11 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{11}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{11}{21} & & \\ & V = \left\{ \frac{11}{21} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (2x-4)& = & -15 \color{red}{+} (-12+x) \\\Leftrightarrow & 6x-12& = &-15-12+x \\\Leftrightarrow & 6x \color{red}{-12} & = &-27 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-27 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 6x-x& = &-27+12 \\\Leftrightarrow & 5x& = &-15 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-15}{ \color{red}{5} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-x-7)& = & -6 \color{red}{-} (-1+3x) \\\Leftrightarrow & -2x-14& = &-6+1-3x \\\Leftrightarrow & -2x \color{red}{-14} & = &-5 \color{red}{-3x} \\\Leftrightarrow & -2x \color{red}{-14} \color{blue}{+14} \color{blue}{+3x} & = &-5 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+14} \\\Leftrightarrow & -2x+3x& = &-5+14 \\\Leftrightarrow & x& = &9 \\ & V = \left\{ 9 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-5x-7)& = & 1 \color{red}{+} (15+x) \\\Leftrightarrow & -10x-14& = &1+15+x \\\Leftrightarrow & -10x \color{red}{-14} & = &16 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{-14} \color{blue}{+14} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{+14} \\\Leftrightarrow & -10x-x& = &16+14 \\\Leftrightarrow & -11x& = &30 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{30}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-30}{11} & & \\ & V = \left\{ \frac{-30}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-6x+6)& = & 10 \color{red}{+} (2+x) \\\Leftrightarrow & -24x+24& = &10+2+x \\\Leftrightarrow & -24x \color{red}{+24} & = &12 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -24x-x& = &12-24 \\\Leftrightarrow & -25x& = &-12 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-12}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{12}{25} & & \\ & V = \left\{ \frac{12}{25} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-6x+5)& = & 15 \color{red}{-} (-3-5x) \\\Leftrightarrow & -18x+15& = &15+3+5x \\\Leftrightarrow & -18x \color{red}{+15} & = &18 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{+15} \color{blue}{-15} \color{blue}{-5x} & = &18 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-15} \\\Leftrightarrow & -18x-5x& = &18-15 \\\Leftrightarrow & -23x& = &3 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{3}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-3}{23} & & \\ & V = \left\{ \frac{-3}{23} \right\} & \\\end{align}\)