Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-2x-7)& = & -12 \color{red}{+} (-11+x) \\\Leftrightarrow & -12x-42& = &-12-11+x \\\Leftrightarrow & -12x \color{red}{-42} & = &-23 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &-23 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & -12x-x& = &-23+42 \\\Leftrightarrow & -13x& = &19 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{19}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-19}{13} & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (x-4)& = & 12 \color{red}{-} (12-2x) \\\Leftrightarrow & 3x-12& = &12-12+2x \\\Leftrightarrow & 3x \color{red}{-12} & = &0 \color{red}{+2x} \\\Leftrightarrow & 3x \color{red}{-12} \color{blue}{+12} \color{blue}{-2x} & = &0 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+12} \\\Leftrightarrow & 3x-2x& = &0+12 \\\Leftrightarrow & x& = &12 \\ & V = \left\{ 12 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (5x+6)& = & -13 \color{red}{-} (12-3x) \\\Leftrightarrow & 10x+12& = &-13-12+3x \\\Leftrightarrow & 10x \color{red}{+12} & = &-25 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+12} \color{blue}{-12} \color{blue}{-3x} & = &-25 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-12} \\\Leftrightarrow & 10x-3x& = &-25-12 \\\Leftrightarrow & 7x& = &-37 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-37}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-37}{7} & & \\ & V = \left\{ \frac{-37}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (x-7)& = & 13 \color{red}{-} (-10+x) \\\Leftrightarrow & 6x-42& = &13+10-x \\\Leftrightarrow & 6x \color{red}{-42} & = &23 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &23 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & 6x+x& = &23+42 \\\Leftrightarrow & 7x& = &65 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{65}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{65}{7} & & \\ & V = \left\{ \frac{65}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-3x-1)& = & -12 \color{red}{+} (8+x) \\\Leftrightarrow & -6x-2& = &-12+8+x \\\Leftrightarrow & -6x \color{red}{-2} & = &-4 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & -6x-x& = &-4+2 \\\Leftrightarrow & -7x& = &-2 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-2}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{2}{7} & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-3x-4)& = & 11 \color{red}{+} (-7-5x) \\\Leftrightarrow & -18x-24& = &11-7-5x \\\Leftrightarrow & -18x \color{red}{-24} & = &4 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-24} \color{blue}{+24} \color{blue}{+5x} & = &4 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+24} \\\Leftrightarrow & -18x+5x& = &4+24 \\\Leftrightarrow & -13x& = &28 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{28}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-28}{13} & & \\ & V = \left\{ \frac{-28}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (2x-5)& = & 14 \color{red}{+} (-5-3x) \\\Leftrightarrow & 4x-10& = &14-5-3x \\\Leftrightarrow & 4x \color{red}{-10} & = &9 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-10} \color{blue}{+10} \color{blue}{+3x} & = &9 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+10} \\\Leftrightarrow & 4x+3x& = &9+10 \\\Leftrightarrow & 7x& = &19 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{19}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{19}{7} & & \\ & V = \left\{ \frac{19}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-x+3)& = & 2 \color{red}{-} (-15+x) \\\Leftrightarrow & -2x+6& = &2+15-x \\\Leftrightarrow & -2x \color{red}{+6} & = &17 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -2x+x& = &17-6 \\\Leftrightarrow & -x& = &11 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{11}{ \color{red}{-1} } \\\Leftrightarrow & x = -11 & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (6x-3)& = & -5 \color{red}{+} (10+x) \\\Leftrightarrow & 36x-18& = &-5+10+x \\\Leftrightarrow & 36x \color{red}{-18} & = &5 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & 36x-x& = &5+18 \\\Leftrightarrow & 35x& = &23 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{23}{ \color{red}{35} } \\\Leftrightarrow & x = \frac{23}{35} & & \\ & V = \left\{ \frac{23}{35} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-2x-3)& = & -14 \color{red}{-} (-3+3x) \\\Leftrightarrow & -4x-6& = &-14+3-3x \\\Leftrightarrow & -4x \color{red}{-6} & = &-11 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-6} \color{blue}{+6} \color{blue}{+3x} & = &-11 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+6} \\\Leftrightarrow & -4x+3x& = &-11+6 \\\Leftrightarrow & -x& = &-5 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-5}{ \color{red}{-1} } \\\Leftrightarrow & x = 5 & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-x+5)& = & 8 \color{red}{-} (-2+x) \\\Leftrightarrow & -4x+20& = &8+2-x \\\Leftrightarrow & -4x \color{red}{+20} & = &10 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & -4x+x& = &10-20 \\\Leftrightarrow & -3x& = &-10 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-10}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{10}{3} & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (5x-2)& = & -15 \color{red}{+} (12+x) \\\Leftrightarrow & 20x-8& = &-15+12+x \\\Leftrightarrow & 20x \color{red}{-8} & = &-3 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & 20x-x& = &-3+8 \\\Leftrightarrow & 19x& = &5 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{5}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{5}{19} & & \\ & V = \left\{ \frac{5}{19} \right\} & \\\end{align}\)