Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-5x+3)& = & 6 \color{red}{-} (6+x) \\\Leftrightarrow & -30x+18& = &6-6-x \\\Leftrightarrow & -30x \color{red}{+18} & = &0 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -30x+x& = &0-18 \\\Leftrightarrow & -29x& = &-18 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-18}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{18}{29} & & \\ & V = \left\{ \frac{18}{29} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-5x-3)& = & -6 \color{red}{+} (12+3x) \\\Leftrightarrow & -10x-6& = &-6+12+3x \\\Leftrightarrow & -10x \color{red}{-6} & = &6 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-6} \color{blue}{+6} \color{blue}{-3x} & = &6 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+6} \\\Leftrightarrow & -10x-3x& = &6+6 \\\Leftrightarrow & -13x& = &12 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{12}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-12}{13} & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (5x+6)& = & 10 \color{red}{+} (12-4x) \\\Leftrightarrow & 25x+30& = &10+12-4x \\\Leftrightarrow & 25x \color{red}{+30} & = &22 \color{red}{-4x} \\\Leftrightarrow & 25x \color{red}{+30} \color{blue}{-30} \color{blue}{+4x} & = &22 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-30} \\\Leftrightarrow & 25x+4x& = &22-30 \\\Leftrightarrow & 29x& = &-8 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-8}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-8}{29} & & \\ & V = \left\{ \frac{-8}{29} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (2x+4)& = & 10 \color{red}{-} (9+x) \\\Leftrightarrow & 6x+12& = &10-9-x \\\Leftrightarrow & 6x \color{red}{+12} & = &1 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 6x+x& = &1-12 \\\Leftrightarrow & 7x& = &-11 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-11}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-11}{7} & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (x+4)& = & 8 \color{red}{-} (6+3x) \\\Leftrightarrow & 5x+20& = &8-6-3x \\\Leftrightarrow & 5x \color{red}{+20} & = &2 \color{red}{-3x} \\\Leftrightarrow & 5x \color{red}{+20} \color{blue}{-20} \color{blue}{+3x} & = &2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-20} \\\Leftrightarrow & 5x+3x& = &2-20 \\\Leftrightarrow & 8x& = &-18 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{-18}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{-9}{4} & & \\ & V = \left\{ \frac{-9}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-6x-3)& = & -14 \color{red}{-} (-1+x) \\\Leftrightarrow & -30x-15& = &-14+1-x \\\Leftrightarrow & -30x \color{red}{-15} & = &-13 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & -30x+x& = &-13+15 \\\Leftrightarrow & -29x& = &2 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{2}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-2}{29} & & \\ & V = \left\{ \frac{-2}{29} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-x-1)& = & -2 \color{red}{-} (-7+x) \\\Leftrightarrow & -5x-5& = &-2+7-x \\\Leftrightarrow & -5x \color{red}{-5} & = &5 \color{red}{-x} \\\Leftrightarrow & -5x \color{red}{-5} \color{blue}{+5} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{+5} \\\Leftrightarrow & -5x+x& = &5+5 \\\Leftrightarrow & -4x& = &10 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{10}{ \color{red}{-4} } \\\Leftrightarrow & x = \frac{-5}{2} & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-2x+5)& = & -3 \color{red}{-} (4-3x) \\\Leftrightarrow & -10x+25& = &-3-4+3x \\\Leftrightarrow & -10x \color{red}{+25} & = &-7 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+25} \color{blue}{-25} \color{blue}{-3x} & = &-7 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-25} \\\Leftrightarrow & -10x-3x& = &-7-25 \\\Leftrightarrow & -13x& = &-32 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-32}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{32}{13} & & \\ & V = \left\{ \frac{32}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (3x+5)& = & 14 \color{red}{-} (-15+x) \\\Leftrightarrow & 18x+30& = &14+15-x \\\Leftrightarrow & 18x \color{red}{+30} & = &29 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &29 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & 18x+x& = &29-30 \\\Leftrightarrow & 19x& = &-1 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-1}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-1}{19} & & \\ & V = \left\{ \frac{-1}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-2x-4)& = & 7 \color{red}{-} (-15-3x) \\\Leftrightarrow & -4x-8& = &7+15+3x \\\Leftrightarrow & -4x \color{red}{-8} & = &22 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-8} \color{blue}{+8} \color{blue}{-3x} & = &22 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+8} \\\Leftrightarrow & -4x-3x& = &22+8 \\\Leftrightarrow & -7x& = &30 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{30}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-30}{7} & & \\ & V = \left\{ \frac{-30}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (x+1)& = & 10 \color{red}{+} (2-4x) \\\Leftrightarrow & 5x+5& = &10+2-4x \\\Leftrightarrow & 5x \color{red}{+5} & = &12 \color{red}{-4x} \\\Leftrightarrow & 5x \color{red}{+5} \color{blue}{-5} \color{blue}{+4x} & = &12 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-5} \\\Leftrightarrow & 5x+4x& = &12-5 \\\Leftrightarrow & 9x& = &7 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{7}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{7}{9} & & \\ & V = \left\{ \frac{7}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (2x+4)& = & 10 \color{red}{-} (8+x) \\\Leftrightarrow & 8x+16& = &10-8-x \\\Leftrightarrow & 8x \color{red}{+16} & = &2 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & 8x+x& = &2-16 \\\Leftrightarrow & 9x& = &-14 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-14}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-14}{9} & & \\ & V = \left\{ \frac{-14}{9} \right\} & \\\end{align}\)