Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (x-5)& = & 9 \color{red}{-} (-4+x) \\\Leftrightarrow & 2x-10& = &9+4-x \\\Leftrightarrow & 2x \color{red}{-10} & = &13 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 2x+x& = &13+10 \\\Leftrightarrow & 3x& = &23 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{23}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{23}{3} & & \\ & V = \left\{ \frac{23}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-4x+2)& = & -4 \color{red}{-} (-5+x) \\\Leftrightarrow & -12x+6& = &-4+5-x \\\Leftrightarrow & -12x \color{red}{+6} & = &1 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -12x+x& = &1-6 \\\Leftrightarrow & -11x& = &-5 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-5}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{5}{11} & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (2x-5)& = & -11 \color{red}{-} (-14-3x) \\\Leftrightarrow & 10x-25& = &-11+14+3x \\\Leftrightarrow & 10x \color{red}{-25} & = &3 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-25} \color{blue}{+25} \color{blue}{-3x} & = &3 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+25} \\\Leftrightarrow & 10x-3x& = &3+25 \\\Leftrightarrow & 7x& = &28 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{28}{ \color{red}{7} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (3x-4)& = & -5 \color{red}{-} (-6+x) \\\Leftrightarrow & 6x-8& = &-5+6-x \\\Leftrightarrow & 6x \color{red}{-8} & = &1 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 6x+x& = &1+8 \\\Leftrightarrow & 7x& = &9 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{9}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{9}{7} & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-6x+2)& = & -4 \color{red}{+} (-1+x) \\\Leftrightarrow & -18x+6& = &-4-1+x \\\Leftrightarrow & -18x \color{red}{+6} & = &-5 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -18x-x& = &-5-6 \\\Leftrightarrow & -19x& = &-11 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-11}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{11}{19} & & \\ & V = \left\{ \frac{11}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-4x-2)& = & 12 \color{red}{+} (-15+3x) \\\Leftrightarrow & -16x-8& = &12-15+3x \\\Leftrightarrow & -16x \color{red}{-8} & = &-3 \color{red}{+3x} \\\Leftrightarrow & -16x \color{red}{-8} \color{blue}{+8} \color{blue}{-3x} & = &-3 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+8} \\\Leftrightarrow & -16x-3x& = &-3+8 \\\Leftrightarrow & -19x& = &5 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{5}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-5}{19} & & \\ & V = \left\{ \frac{-5}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (2x+4)& = & -6 \color{red}{+} (9+x) \\\Leftrightarrow & 10x+20& = &-6+9+x \\\Leftrightarrow & 10x \color{red}{+20} & = &3 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 10x-x& = &3-20 \\\Leftrightarrow & 9x& = &-17 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-17}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-17}{9} & & \\ & V = \left\{ \frac{-17}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-5x+2)& = & -15 \color{red}{+} (3+x) \\\Leftrightarrow & -20x+8& = &-15+3+x \\\Leftrightarrow & -20x \color{red}{+8} & = &-12 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -20x-x& = &-12-8 \\\Leftrightarrow & -21x& = &-20 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-20}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{20}{21} & & \\ & V = \left\{ \frac{20}{21} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (6x+2)& = & -15 \color{red}{-} (-6+x) \\\Leftrightarrow & 24x+8& = &-15+6-x \\\Leftrightarrow & 24x \color{red}{+8} & = &-9 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 24x+x& = &-9-8 \\\Leftrightarrow & 25x& = &-17 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-17}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-17}{25} & & \\ & V = \left\{ \frac{-17}{25} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-5x-2)& = & 14 \color{red}{+} (4+x) \\\Leftrightarrow & -25x-10& = &14+4+x \\\Leftrightarrow & -25x \color{red}{-10} & = &18 \color{red}{+x} \\\Leftrightarrow & -25x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &18 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & -25x-x& = &18+10 \\\Leftrightarrow & -26x& = &28 \\\Leftrightarrow & \frac{-26x}{ \color{red}{-26} }& = &\frac{28}{ \color{red}{-26} } \\\Leftrightarrow & x = \frac{-14}{13} & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (6x+1)& = & -3 \color{red}{+} (14+x) \\\Leftrightarrow & 24x+4& = &-3+14+x \\\Leftrightarrow & 24x \color{red}{+4} & = &11 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 24x-x& = &11-4 \\\Leftrightarrow & 23x& = &7 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{7}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{7}{23} & & \\ & V = \left\{ \frac{7}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-3x+7)& = & 2 \color{red}{+} (4-4x) \\\Leftrightarrow & -9x+21& = &2+4-4x \\\Leftrightarrow & -9x \color{red}{+21} & = &6 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{+21} \color{blue}{-21} \color{blue}{+4x} & = &6 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-21} \\\Leftrightarrow & -9x+4x& = &6-21 \\\Leftrightarrow & -5x& = &-15 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-15}{ \color{red}{-5} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)