Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (5x-7)& = & -9 \color{red}{+} (14-3x) \\\Leftrightarrow & 10x-14& = &-9+14-3x \\\Leftrightarrow & 10x \color{red}{-14} & = &5 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-14} \color{blue}{+14} \color{blue}{+3x} & = &5 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+14} \\\Leftrightarrow & 10x+3x& = &5+14 \\\Leftrightarrow & 13x& = &19 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{19}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{19}{13} & & \\ & V = \left\{ \frac{19}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (5x-4)& = & 6 \color{red}{-} (8-3x) \\\Leftrightarrow & 10x-8& = &6-8+3x \\\Leftrightarrow & 10x \color{red}{-8} & = &-2 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-8} \color{blue}{+8} \color{blue}{-3x} & = &-2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+8} \\\Leftrightarrow & 10x-3x& = &-2+8 \\\Leftrightarrow & 7x& = &6 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{6}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{6}{7} & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-4x+2)& = & 2 \color{red}{+} (-6+x) \\\Leftrightarrow & -16x+8& = &2-6+x \\\Leftrightarrow & -16x \color{red}{+8} & = &-4 \color{red}{+x} \\\Leftrightarrow & -16x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -16x-x& = &-4-8 \\\Leftrightarrow & -17x& = &-12 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-12}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{12}{17} & & \\ & V = \left\{ \frac{12}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-4x-1)& = & 7 \color{red}{-} (13+x) \\\Leftrightarrow & -20x-5& = &7-13-x \\\Leftrightarrow & -20x \color{red}{-5} & = &-6 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-5} \color{blue}{+5} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{+5} \\\Leftrightarrow & -20x+x& = &-6+5 \\\Leftrightarrow & -19x& = &-1 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-1}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{1}{19} & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-2x-3)& = & 3 \color{red}{+} (-6+x) \\\Leftrightarrow & -12x-18& = &3-6+x \\\Leftrightarrow & -12x \color{red}{-18} & = &-3 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & -12x-x& = &-3+18 \\\Leftrightarrow & -13x& = &15 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{15}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-15}{13} & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-3x-5)& = & 13 \color{red}{+} (10-4x) \\\Leftrightarrow & -9x-15& = &13+10-4x \\\Leftrightarrow & -9x \color{red}{-15} & = &23 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{-15} \color{blue}{+15} \color{blue}{+4x} & = &23 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+15} \\\Leftrightarrow & -9x+4x& = &23+15 \\\Leftrightarrow & -5x& = &38 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{38}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-38}{5} & & \\ & V = \left\{ \frac{-38}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (6x+3)& = & -14 \color{red}{+} (-13+x) \\\Leftrightarrow & 24x+12& = &-14-13+x \\\Leftrightarrow & 24x \color{red}{+12} & = &-27 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-27 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 24x-x& = &-27-12 \\\Leftrightarrow & 23x& = &-39 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-39}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-39}{23} & & \\ & V = \left\{ \frac{-39}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-x-7)& = & -9 \color{red}{-} (6+x) \\\Leftrightarrow & -6x-42& = &-9-6-x \\\Leftrightarrow & -6x \color{red}{-42} & = &-15 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &-15 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & -6x+x& = &-15+42 \\\Leftrightarrow & -5x& = &27 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{27}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-27}{5} & & \\ & V = \left\{ \frac{-27}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-x+1)& = & 13 \color{red}{+} (-10+x) \\\Leftrightarrow & -2x+2& = &13-10+x \\\Leftrightarrow & -2x \color{red}{+2} & = &3 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{+2} \color{blue}{-2} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{-2} \\\Leftrightarrow & -2x-x& = &3-2 \\\Leftrightarrow & -3x& = &1 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{1}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-1}{3} & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-2x+4)& = & -14 \color{red}{+} (15+x) \\\Leftrightarrow & -10x+20& = &-14+15+x \\\Leftrightarrow & -10x \color{red}{+20} & = &1 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & -10x-x& = &1-20 \\\Leftrightarrow & -11x& = &-19 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-19}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{19}{11} & & \\ & V = \left\{ \frac{19}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (4x+7)& = & -3 \color{red}{-} (9+x) \\\Leftrightarrow & 12x+21& = &-3-9-x \\\Leftrightarrow & 12x \color{red}{+21} & = &-12 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+21} \color{blue}{-21} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{-21} \\\Leftrightarrow & 12x+x& = &-12-21 \\\Leftrightarrow & 13x& = &-33 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-33}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-33}{13} & & \\ & V = \left\{ \frac{-33}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-3x-6)& = & -9 \color{red}{+} (-11+x) \\\Leftrightarrow & -12x-24& = &-9-11+x \\\Leftrightarrow & -12x \color{red}{-24} & = &-20 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-20 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -12x-x& = &-20+24 \\\Leftrightarrow & -13x& = &4 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{4}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-4}{13} & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)