Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-3x+3)& = & -9 \color{red}{-} (13-5x) \\\Leftrightarrow & -18x+18& = &-9-13+5x \\\Leftrightarrow & -18x \color{red}{+18} & = &-22 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{+18} \color{blue}{-18} \color{blue}{-5x} & = &-22 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-18} \\\Leftrightarrow & -18x-5x& = &-22-18 \\\Leftrightarrow & -23x& = &-40 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-40}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{40}{23} & & \\ & V = \left\{ \frac{40}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-5x+6)& = & -1 \color{red}{+} (5+x) \\\Leftrightarrow & -10x+12& = &-1+5+x \\\Leftrightarrow & -10x \color{red}{+12} & = &4 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -10x-x& = &4-12 \\\Leftrightarrow & -11x& = &-8 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-8}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{8}{11} & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (2x+2)& = & 14 \color{red}{+} (-12+x) \\\Leftrightarrow & 6x+6& = &14-12+x \\\Leftrightarrow & 6x \color{red}{+6} & = &2 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 6x-x& = &2-6 \\\Leftrightarrow & 5x& = &-4 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-4}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-4}{5} & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (4x-7)& = & 8 \color{red}{+} (1+x) \\\Leftrightarrow & 20x-35& = &8+1+x \\\Leftrightarrow & 20x \color{red}{-35} & = &9 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-35} \color{blue}{+35} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{+35} \\\Leftrightarrow & 20x-x& = &9+35 \\\Leftrightarrow & 19x& = &44 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{44}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{44}{19} & & \\ & V = \left\{ \frac{44}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-4x-1)& = & 7 \color{red}{+} (13+x) \\\Leftrightarrow & -24x-6& = &7+13+x \\\Leftrightarrow & -24x \color{red}{-6} & = &20 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &20 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -24x-x& = &20+6 \\\Leftrightarrow & -25x& = &26 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{26}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-26}{25} & & \\ & V = \left\{ \frac{-26}{25} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (6x-1)& = & 11 \color{red}{-} (4+x) \\\Leftrightarrow & 12x-2& = &11-4-x \\\Leftrightarrow & 12x \color{red}{-2} & = &7 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & 12x+x& = &7+2 \\\Leftrightarrow & 13x& = &9 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{9}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{9}{13} & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (3x+3)& = & 6 \color{red}{-} (-8+4x) \\\Leftrightarrow & 9x+9& = &6+8-4x \\\Leftrightarrow & 9x \color{red}{+9} & = &14 \color{red}{-4x} \\\Leftrightarrow & 9x \color{red}{+9} \color{blue}{-9} \color{blue}{+4x} & = &14 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-9} \\\Leftrightarrow & 9x+4x& = &14-9 \\\Leftrightarrow & 13x& = &5 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{5}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{5}{13} & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (3x-2)& = & 6 \color{red}{+} (-2-5x) \\\Leftrightarrow & 18x-12& = &6-2-5x \\\Leftrightarrow & 18x \color{red}{-12} & = &4 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-12} \color{blue}{+12} \color{blue}{+5x} & = &4 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+12} \\\Leftrightarrow & 18x+5x& = &4+12 \\\Leftrightarrow & 23x& = &16 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{16}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{16}{23} & & \\ & V = \left\{ \frac{16}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-6x-3)& = & -3 \color{red}{-} (-14+x) \\\Leftrightarrow & -24x-12& = &-3+14-x \\\Leftrightarrow & -24x \color{red}{-12} & = &11 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -24x+x& = &11+12 \\\Leftrightarrow & -23x& = &23 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{23}{ \color{red}{-23} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (5x+3)& = & -13 \color{red}{-} (8+x) \\\Leftrightarrow & 20x+12& = &-13-8-x \\\Leftrightarrow & 20x \color{red}{+12} & = &-21 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-21 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 20x+x& = &-21-12 \\\Leftrightarrow & 21x& = &-33 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-33}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-11}{7} & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-5x+5)& = & -3 \color{red}{-} (-9+x) \\\Leftrightarrow & -15x+15& = &-3+9-x \\\Leftrightarrow & -15x \color{red}{+15} & = &6 \color{red}{-x} \\\Leftrightarrow & -15x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & -15x+x& = &6-15 \\\Leftrightarrow & -14x& = &-9 \\\Leftrightarrow & \frac{-14x}{ \color{red}{-14} }& = &\frac{-9}{ \color{red}{-14} } \\\Leftrightarrow & x = \frac{9}{14} & & \\ & V = \left\{ \frac{9}{14} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-2x+5)& = & -11 \color{red}{-} (-11-5x) \\\Leftrightarrow & -8x+20& = &-11+11+5x \\\Leftrightarrow & -8x \color{red}{+20} & = &0 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{+20} \color{blue}{-20} \color{blue}{-5x} & = &0 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-20} \\\Leftrightarrow & -8x-5x& = &0-20 \\\Leftrightarrow & -13x& = &-20 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-20}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{20}{13} & & \\ & V = \left\{ \frac{20}{13} \right\} & \\\end{align}\)