Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (4x-2)& = & -10 \color{red}{+} (5-5x) \\\Leftrightarrow & 16x-8& = &-10+5-5x \\\Leftrightarrow & 16x \color{red}{-8} & = &-5 \color{red}{-5x} \\\Leftrightarrow & 16x \color{red}{-8} \color{blue}{+8} \color{blue}{+5x} & = &-5 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+8} \\\Leftrightarrow & 16x+5x& = &-5+8 \\\Leftrightarrow & 21x& = &3 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{3}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{1}{7} & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-4x+2)& = & 15 \color{red}{+} (13+x) \\\Leftrightarrow & -12x+6& = &15+13+x \\\Leftrightarrow & -12x \color{red}{+6} & = &28 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &28 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -12x-x& = &28-6 \\\Leftrightarrow & -13x& = &22 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{22}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-22}{13} & & \\ & V = \left\{ \frac{-22}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (2x-7)& = & 7 \color{red}{-} (9+x) \\\Leftrightarrow & 6x-21& = &7-9-x \\\Leftrightarrow & 6x \color{red}{-21} & = &-2 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-21} \color{blue}{+21} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+21} \\\Leftrightarrow & 6x+x& = &-2+21 \\\Leftrightarrow & 7x& = &19 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{19}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{19}{7} & & \\ & V = \left\{ \frac{19}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-6x-6)& = & 7 \color{red}{+} (-12+x) \\\Leftrightarrow & -36x-36& = &7-12+x \\\Leftrightarrow & -36x \color{red}{-36} & = &-5 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & -36x-x& = &-5+36 \\\Leftrightarrow & -37x& = &31 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{31}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{-31}{37} & & \\ & V = \left\{ \frac{-31}{37} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (5x+7)& = & -13 \color{red}{-} (-6+4x) \\\Leftrightarrow & 15x+21& = &-13+6-4x \\\Leftrightarrow & 15x \color{red}{+21} & = &-7 \color{red}{-4x} \\\Leftrightarrow & 15x \color{red}{+21} \color{blue}{-21} \color{blue}{+4x} & = &-7 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-21} \\\Leftrightarrow & 15x+4x& = &-7-21 \\\Leftrightarrow & 19x& = &-28 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-28}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-28}{19} & & \\ & V = \left\{ \frac{-28}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (x-2)& = & -10 \color{red}{+} (4-3x) \\\Leftrightarrow & 4x-8& = &-10+4-3x \\\Leftrightarrow & 4x \color{red}{-8} & = &-6 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-8} \color{blue}{+8} \color{blue}{+3x} & = &-6 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+8} \\\Leftrightarrow & 4x+3x& = &-6+8 \\\Leftrightarrow & 7x& = &2 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{2}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{2}{7} & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (6x-6)& = & -10 \color{red}{-} (11-5x) \\\Leftrightarrow & 18x-18& = &-10-11+5x \\\Leftrightarrow & 18x \color{red}{-18} & = &-21 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-18} \color{blue}{+18} \color{blue}{-5x} & = &-21 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+18} \\\Leftrightarrow & 18x-5x& = &-21+18 \\\Leftrightarrow & 13x& = &-3 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-3}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-3}{13} & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-x-6)& = & -7 \color{red}{+} (8+x) \\\Leftrightarrow & -6x-36& = &-7+8+x \\\Leftrightarrow & -6x \color{red}{-36} & = &1 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & -6x-x& = &1+36 \\\Leftrightarrow & -7x& = &37 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{37}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-37}{7} & & \\ & V = \left\{ \frac{-37}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (4x+5)& = & 3 \color{red}{-} (5+x) \\\Leftrightarrow & 8x+10& = &3-5-x \\\Leftrightarrow & 8x \color{red}{+10} & = &-2 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & 8x+x& = &-2-10 \\\Leftrightarrow & 9x& = &-12 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-12}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-4}{3} & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (3x-3)& = & 5 \color{red}{+} (8-2x) \\\Leftrightarrow & 15x-15& = &5+8-2x \\\Leftrightarrow & 15x \color{red}{-15} & = &13 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-15} \color{blue}{+15} \color{blue}{+2x} & = &13 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+15} \\\Leftrightarrow & 15x+2x& = &13+15 \\\Leftrightarrow & 17x& = &28 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{28}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{28}{17} & & \\ & V = \left\{ \frac{28}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-2x+3)& = & -10 \color{red}{+} (1+x) \\\Leftrightarrow & -12x+18& = &-10+1+x \\\Leftrightarrow & -12x \color{red}{+18} & = &-9 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & -12x-x& = &-9-18 \\\Leftrightarrow & -13x& = &-27 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-27}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{27}{13} & & \\ & V = \left\{ \frac{27}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (2x+7)& = & 6 \color{red}{+} (-5+x) \\\Leftrightarrow & 12x+42& = &6-5+x \\\Leftrightarrow & 12x \color{red}{+42} & = &1 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & 12x-x& = &1-42 \\\Leftrightarrow & 11x& = &-41 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-41}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-41}{11} & & \\ & V = \left\{ \frac{-41}{11} \right\} & \\\end{align}\)