Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-2x+5)& = & -1 \color{red}{-} (15+x) \\\Leftrightarrow & -6x+15& = &-1-15-x \\\Leftrightarrow & -6x \color{red}{+15} & = &-16 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &-16 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & -6x+x& = &-16-15 \\\Leftrightarrow & -5x& = &-31 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-31}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{31}{5} & & \\ & V = \left\{ \frac{31}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-2x+2)& = & -6 \color{red}{+} (-6+x) \\\Leftrightarrow & -10x+10& = &-6-6+x \\\Leftrightarrow & -10x \color{red}{+10} & = &-12 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & -10x-x& = &-12-10 \\\Leftrightarrow & -11x& = &-22 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-22}{ \color{red}{-11} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-4x+7)& = & 6 \color{red}{+} (10+x) \\\Leftrightarrow & -12x+21& = &6+10+x \\\Leftrightarrow & -12x \color{red}{+21} & = &16 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+21} \color{blue}{-21} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{-21} \\\Leftrightarrow & -12x-x& = &16-21 \\\Leftrightarrow & -13x& = &-5 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-5}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{5}{13} & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (3x+2)& = & 9 \color{red}{+} (4-5x) \\\Leftrightarrow & 6x+4& = &9+4-5x \\\Leftrightarrow & 6x \color{red}{+4} & = &13 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+4} \color{blue}{-4} \color{blue}{+5x} & = &13 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-4} \\\Leftrightarrow & 6x+5x& = &13-4 \\\Leftrightarrow & 11x& = &9 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{9}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{9}{11} & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (x-2)& = & -12 \color{red}{+} (3-3x) \\\Leftrightarrow & 4x-8& = &-12+3-3x \\\Leftrightarrow & 4x \color{red}{-8} & = &-9 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-8} \color{blue}{+8} \color{blue}{+3x} & = &-9 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+8} \\\Leftrightarrow & 4x+3x& = &-9+8 \\\Leftrightarrow & 7x& = &-1 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-1}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-1}{7} & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-5x+7)& = & 10 \color{red}{+} (-3-3x) \\\Leftrightarrow & -10x+14& = &10-3-3x \\\Leftrightarrow & -10x \color{red}{+14} & = &7 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{+14} \color{blue}{-14} \color{blue}{+3x} & = &7 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-14} \\\Leftrightarrow & -10x+3x& = &7-14 \\\Leftrightarrow & -7x& = &-7 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-7}{ \color{red}{-7} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-6x-1)& = & 5 \color{red}{-} (-8+x) \\\Leftrightarrow & -24x-4& = &5+8-x \\\Leftrightarrow & -24x \color{red}{-4} & = &13 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & -24x+x& = &13+4 \\\Leftrightarrow & -23x& = &17 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{17}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-17}{23} & & \\ & V = \left\{ \frac{-17}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-4x+2)& = & 5 \color{red}{+} (15+x) \\\Leftrightarrow & -16x+8& = &5+15+x \\\Leftrightarrow & -16x \color{red}{+8} & = &20 \color{red}{+x} \\\Leftrightarrow & -16x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &20 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -16x-x& = &20-8 \\\Leftrightarrow & -17x& = &12 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{12}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-12}{17} & & \\ & V = \left\{ \frac{-12}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-3x+1)& = & 1 \color{red}{+} (15+x) \\\Leftrightarrow & -18x+6& = &1+15+x \\\Leftrightarrow & -18x \color{red}{+6} & = &16 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -18x-x& = &16-6 \\\Leftrightarrow & -19x& = &10 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{10}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-10}{19} & & \\ & V = \left\{ \frac{-10}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (2x+2)& = & -5 \color{red}{+} (-6+x) \\\Leftrightarrow & 6x+6& = &-5-6+x \\\Leftrightarrow & 6x \color{red}{+6} & = &-11 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 6x-x& = &-11-6 \\\Leftrightarrow & 5x& = &-17 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-17}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-17}{5} & & \\ & V = \left\{ \frac{-17}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-3x+7)& = & -6 \color{red}{-} (-9-5x) \\\Leftrightarrow & -18x+42& = &-6+9+5x \\\Leftrightarrow & -18x \color{red}{+42} & = &3 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{+42} \color{blue}{-42} \color{blue}{-5x} & = &3 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-42} \\\Leftrightarrow & -18x-5x& = &3-42 \\\Leftrightarrow & -23x& = &-39 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-39}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{39}{23} & & \\ & V = \left\{ \frac{39}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-2x+3)& = & 11 \color{red}{-} (5+x) \\\Leftrightarrow & -12x+18& = &11-5-x \\\Leftrightarrow & -12x \color{red}{+18} & = &6 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -12x+x& = &6-18 \\\Leftrightarrow & -11x& = &-12 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-12}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{12}{11} & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)