Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (x+5)& = & -3 \color{red}{+} (-10+x) \\\Leftrightarrow & 4x+20& = &-3-10+x \\\Leftrightarrow & 4x \color{red}{+20} & = &-13 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 4x-x& = &-13-20 \\\Leftrightarrow & 3x& = &-33 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-33}{ \color{red}{3} } \\\Leftrightarrow & x = -11 & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (4x-3)& = & -14 \color{red}{-} (13+x) \\\Leftrightarrow & 12x-9& = &-14-13-x \\\Leftrightarrow & 12x \color{red}{-9} & = &-27 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-9} \color{blue}{+9} \color{blue}{+x} & = &-27 \color{red}{-x} \color{blue}{+x} \color{blue}{+9} \\\Leftrightarrow & 12x+x& = &-27+9 \\\Leftrightarrow & 13x& = &-18 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-18}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-18}{13} & & \\ & V = \left\{ \frac{-18}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-4x+3)& = & 10 \color{red}{-} (-7+x) \\\Leftrightarrow & -24x+18& = &10+7-x \\\Leftrightarrow & -24x \color{red}{+18} & = &17 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -24x+x& = &17-18 \\\Leftrightarrow & -23x& = &-1 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-1}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{1}{23} & & \\ & V = \left\{ \frac{1}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (5x-6)& = & -11 \color{red}{+} (1+x) \\\Leftrightarrow & 10x-12& = &-11+1+x \\\Leftrightarrow & 10x \color{red}{-12} & = &-10 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 10x-x& = &-10+12 \\\Leftrightarrow & 9x& = &2 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{2}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{2}{9} & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-2x+6)& = & -13 \color{red}{+} (-4-3x) \\\Leftrightarrow & -10x+30& = &-13-4-3x \\\Leftrightarrow & -10x \color{red}{+30} & = &-17 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{+30} \color{blue}{-30} \color{blue}{+3x} & = &-17 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-30} \\\Leftrightarrow & -10x+3x& = &-17-30 \\\Leftrightarrow & -7x& = &-47 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-47}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{47}{7} & & \\ & V = \left\{ \frac{47}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-6x-3)& = & -8 \color{red}{+} (5+x) \\\Leftrightarrow & -18x-9& = &-8+5+x \\\Leftrightarrow & -18x \color{red}{-9} & = &-3 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-9} \color{blue}{+9} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{+9} \\\Leftrightarrow & -18x-x& = &-3+9 \\\Leftrightarrow & -19x& = &6 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{6}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-6}{19} & & \\ & V = \left\{ \frac{-6}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-4x-6)& = & 13 \color{red}{+} (1+x) \\\Leftrightarrow & -20x-30& = &13+1+x \\\Leftrightarrow & -20x \color{red}{-30} & = &14 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & -20x-x& = &14+30 \\\Leftrightarrow & -21x& = &44 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{44}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-44}{21} & & \\ & V = \left\{ \frac{-44}{21} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-6x+3)& = & -11 \color{red}{+} (14-5x) \\\Leftrightarrow & -18x+9& = &-11+14-5x \\\Leftrightarrow & -18x \color{red}{+9} & = &3 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{+9} \color{blue}{-9} \color{blue}{+5x} & = &3 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-9} \\\Leftrightarrow & -18x+5x& = &3-9 \\\Leftrightarrow & -13x& = &-6 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-6}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{6}{13} & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-6x-1)& = & -2 \color{red}{-} (8+x) \\\Leftrightarrow & -30x-5& = &-2-8-x \\\Leftrightarrow & -30x \color{red}{-5} & = &-10 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-5} \color{blue}{+5} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{+5} \\\Leftrightarrow & -30x+x& = &-10+5 \\\Leftrightarrow & -29x& = &-5 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-5}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{5}{29} & & \\ & V = \left\{ \frac{5}{29} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-4x+3)& = & 2 \color{red}{-} (-4+x) \\\Leftrightarrow & -8x+6& = &2+4-x \\\Leftrightarrow & -8x \color{red}{+6} & = &6 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -8x+x& = &6-6 \\\Leftrightarrow & -7x& = &0 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{0}{ \color{red}{-7} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (5x-7)& = & 1 \color{red}{+} (10-3x) \\\Leftrightarrow & 10x-14& = &1+10-3x \\\Leftrightarrow & 10x \color{red}{-14} & = &11 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-14} \color{blue}{+14} \color{blue}{+3x} & = &11 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+14} \\\Leftrightarrow & 10x+3x& = &11+14 \\\Leftrightarrow & 13x& = &25 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{25}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{25}{13} & & \\ & V = \left\{ \frac{25}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (x+1)& = & -6 \color{red}{-} (-7-5x) \\\Leftrightarrow & 6x+6& = &-6+7+5x \\\Leftrightarrow & 6x \color{red}{+6} & = &1 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+6} \color{blue}{-6} \color{blue}{-5x} & = &1 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-6} \\\Leftrightarrow & 6x-5x& = &1-6 \\\Leftrightarrow & x& = &-5 \\ & V = \left\{ -5 \right\} & \\\end{align}\)