Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-6x-6)& = & 3 \color{red}{-} (2+x) \\\Leftrightarrow & -12x-12& = &3-2-x \\\Leftrightarrow & -12x \color{red}{-12} & = &1 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -12x+x& = &1+12 \\\Leftrightarrow & -11x& = &13 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{13}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-13}{11} & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-3x+2)& = & 5 \color{red}{+} (-15-4x) \\\Leftrightarrow & -9x+6& = &5-15-4x \\\Leftrightarrow & -9x \color{red}{+6} & = &-10 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{+6} \color{blue}{-6} \color{blue}{+4x} & = &-10 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-6} \\\Leftrightarrow & -9x+4x& = &-10-6 \\\Leftrightarrow & -5x& = &-16 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-16}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{16}{5} & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (5x-4)& = & 11 \color{red}{-} (8+2x) \\\Leftrightarrow & 25x-20& = &11-8-2x \\\Leftrightarrow & 25x \color{red}{-20} & = &3 \color{red}{-2x} \\\Leftrightarrow & 25x \color{red}{-20} \color{blue}{+20} \color{blue}{+2x} & = &3 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+20} \\\Leftrightarrow & 25x+2x& = &3+20 \\\Leftrightarrow & 27x& = &23 \\\Leftrightarrow & \frac{27x}{ \color{red}{27} }& = &\frac{23}{ \color{red}{27} } \\\Leftrightarrow & x = \frac{23}{27} & & \\ & V = \left\{ \frac{23}{27} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (4x-7)& = & -6 \color{red}{+} (1+x) \\\Leftrightarrow & 12x-21& = &-6+1+x \\\Leftrightarrow & 12x \color{red}{-21} & = &-5 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-21} \color{blue}{+21} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+21} \\\Leftrightarrow & 12x-x& = &-5+21 \\\Leftrightarrow & 11x& = &16 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{16}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{16}{11} & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (4x-2)& = & -10 \color{red}{-} (-5+3x) \\\Leftrightarrow & 16x-8& = &-10+5-3x \\\Leftrightarrow & 16x \color{red}{-8} & = &-5 \color{red}{-3x} \\\Leftrightarrow & 16x \color{red}{-8} \color{blue}{+8} \color{blue}{+3x} & = &-5 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+8} \\\Leftrightarrow & 16x+3x& = &-5+8 \\\Leftrightarrow & 19x& = &3 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{3}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{3}{19} & & \\ & V = \left\{ \frac{3}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-3x+5)& = & -13 \color{red}{+} (-11+x) \\\Leftrightarrow & -12x+20& = &-13-11+x \\\Leftrightarrow & -12x \color{red}{+20} & = &-24 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &-24 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & -12x-x& = &-24-20 \\\Leftrightarrow & -13x& = &-44 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-44}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{44}{13} & & \\ & V = \left\{ \frac{44}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (5x-4)& = & 14 \color{red}{-} (2+3x) \\\Leftrightarrow & 20x-16& = &14-2-3x \\\Leftrightarrow & 20x \color{red}{-16} & = &12 \color{red}{-3x} \\\Leftrightarrow & 20x \color{red}{-16} \color{blue}{+16} \color{blue}{+3x} & = &12 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+16} \\\Leftrightarrow & 20x+3x& = &12+16 \\\Leftrightarrow & 23x& = &28 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{28}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{28}{23} & & \\ & V = \left\{ \frac{28}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (4x-1)& = & 14 \color{red}{+} (13+x) \\\Leftrightarrow & 24x-6& = &14+13+x \\\Leftrightarrow & 24x \color{red}{-6} & = &27 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &27 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 24x-x& = &27+6 \\\Leftrightarrow & 23x& = &33 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{33}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{33}{23} & & \\ & V = \left\{ \frac{33}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (4x+7)& = & 11 \color{red}{-} (9+x) \\\Leftrightarrow & 20x+35& = &11-9-x \\\Leftrightarrow & 20x \color{red}{+35} & = &2 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+35} \color{blue}{-35} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-35} \\\Leftrightarrow & 20x+x& = &2-35 \\\Leftrightarrow & 21x& = &-33 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-33}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-11}{7} & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (x-2)& = & 2 \color{red}{-} (-6+x) \\\Leftrightarrow & 6x-12& = &2+6-x \\\Leftrightarrow & 6x \color{red}{-12} & = &8 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 6x+x& = &8+12 \\\Leftrightarrow & 7x& = &20 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{20}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{20}{7} & & \\ & V = \left\{ \frac{20}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (4x-7)& = & -7 \color{red}{-} (3+3x) \\\Leftrightarrow & 8x-14& = &-7-3-3x \\\Leftrightarrow & 8x \color{red}{-14} & = &-10 \color{red}{-3x} \\\Leftrightarrow & 8x \color{red}{-14} \color{blue}{+14} \color{blue}{+3x} & = &-10 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+14} \\\Leftrightarrow & 8x+3x& = &-10+14 \\\Leftrightarrow & 11x& = &4 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{4}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{4}{11} & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-3x-3)& = & 14 \color{red}{-} (-14+x) \\\Leftrightarrow & -12x-12& = &14+14-x \\\Leftrightarrow & -12x \color{red}{-12} & = &28 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &28 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -12x+x& = &28+12 \\\Leftrightarrow & -11x& = &40 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{40}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-40}{11} & & \\ & V = \left\{ \frac{-40}{11} \right\} & \\\end{align}\)