Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-2x-4)& = & -10 \color{red}{+} (9+x) \\\Leftrightarrow & -4x-8& = &-10+9+x \\\Leftrightarrow & -4x \color{red}{-8} & = &-1 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -4x-x& = &-1+8 \\\Leftrightarrow & -5x& = &7 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{7}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-7}{5} & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (6x+1)& = & -13 \color{red}{-} (-7+x) \\\Leftrightarrow & 24x+4& = &-13+7-x \\\Leftrightarrow & 24x \color{red}{+4} & = &-6 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 24x+x& = &-6-4 \\\Leftrightarrow & 25x& = &-10 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-10}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-2}{5} & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (4x-7)& = & -12 \color{red}{-} (-5+x) \\\Leftrightarrow & 12x-21& = &-12+5-x \\\Leftrightarrow & 12x \color{red}{-21} & = &-7 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-21} \color{blue}{+21} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{+21} \\\Leftrightarrow & 12x+x& = &-7+21 \\\Leftrightarrow & 13x& = &14 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{14}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{14}{13} & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (3x+2)& = & 7 \color{red}{+} (-8+x) \\\Leftrightarrow & 18x+12& = &7-8+x \\\Leftrightarrow & 18x \color{red}{+12} & = &-1 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 18x-x& = &-1-12 \\\Leftrightarrow & 17x& = &-13 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-13}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-13}{17} & & \\ & V = \left\{ \frac{-13}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (3x+2)& = & -6 \color{red}{+} (-11+x) \\\Leftrightarrow & 12x+8& = &-6-11+x \\\Leftrightarrow & 12x \color{red}{+8} & = &-17 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 12x-x& = &-17-8 \\\Leftrightarrow & 11x& = &-25 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-25}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-25}{11} & & \\ & V = \left\{ \frac{-25}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (6x+2)& = & -4 \color{red}{-} (-15-5x) \\\Leftrightarrow & 18x+6& = &-4+15+5x \\\Leftrightarrow & 18x \color{red}{+6} & = &11 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{+6} \color{blue}{-6} \color{blue}{-5x} & = &11 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-6} \\\Leftrightarrow & 18x-5x& = &11-6 \\\Leftrightarrow & 13x& = &5 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{5}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{5}{13} & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-6x-2)& = & -13 \color{red}{+} (6+x) \\\Leftrightarrow & -24x-8& = &-13+6+x \\\Leftrightarrow & -24x \color{red}{-8} & = &-7 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -24x-x& = &-7+8 \\\Leftrightarrow & -25x& = &1 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{1}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-1}{25} & & \\ & V = \left\{ \frac{-1}{25} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (5x+1)& = & 3 \color{red}{+} (-7+x) \\\Leftrightarrow & 20x+4& = &3-7+x \\\Leftrightarrow & 20x \color{red}{+4} & = &-4 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 20x-x& = &-4-4 \\\Leftrightarrow & 19x& = &-8 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-8}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-8}{19} & & \\ & V = \left\{ \frac{-8}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-2x-7)& = & 1 \color{red}{+} (10-3x) \\\Leftrightarrow & -4x-14& = &1+10-3x \\\Leftrightarrow & -4x \color{red}{-14} & = &11 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-14} \color{blue}{+14} \color{blue}{+3x} & = &11 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+14} \\\Leftrightarrow & -4x+3x& = &11+14 \\\Leftrightarrow & -x& = &25 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{25}{ \color{red}{-1} } \\\Leftrightarrow & x = -25 & & \\ & V = \left\{ -25 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (5x-1)& = & -15 \color{red}{+} (14+x) \\\Leftrightarrow & 30x-6& = &-15+14+x \\\Leftrightarrow & 30x \color{red}{-6} & = &-1 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 30x-x& = &-1+6 \\\Leftrightarrow & 29x& = &5 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{5}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{5}{29} & & \\ & V = \left\{ \frac{5}{29} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (5x-3)& = & 14 \color{red}{+} (-9+x) \\\Leftrightarrow & 20x-12& = &14-9+x \\\Leftrightarrow & 20x \color{red}{-12} & = &5 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 20x-x& = &5+12 \\\Leftrightarrow & 19x& = &17 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{17}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{17}{19} & & \\ & V = \left\{ \frac{17}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-4x+2)& = & 15 \color{red}{+} (10+x) \\\Leftrightarrow & -12x+6& = &15+10+x \\\Leftrightarrow & -12x \color{red}{+6} & = &25 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &25 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -12x-x& = &25-6 \\\Leftrightarrow & -13x& = &19 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{19}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-19}{13} & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)