Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (4x-7)& = & 8 \color{red}{+} (-4+x) \\\Leftrightarrow & 16x-28& = &8-4+x \\\Leftrightarrow & 16x \color{red}{-28} & = &4 \color{red}{+x} \\\Leftrightarrow & 16x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & 16x-x& = &4+28 \\\Leftrightarrow & 15x& = &32 \\\Leftrightarrow & \frac{15x}{ \color{red}{15} }& = &\frac{32}{ \color{red}{15} } \\\Leftrightarrow & x = \frac{32}{15} & & \\ & V = \left\{ \frac{32}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (x-2)& = & 4 \color{red}{+} (5-2x) \\\Leftrightarrow & 3x-6& = &4+5-2x \\\Leftrightarrow & 3x \color{red}{-6} & = &9 \color{red}{-2x} \\\Leftrightarrow & 3x \color{red}{-6} \color{blue}{+6} \color{blue}{+2x} & = &9 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+6} \\\Leftrightarrow & 3x+2x& = &9+6 \\\Leftrightarrow & 5x& = &15 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{15}{ \color{red}{5} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (6x-2)& = & -11 \color{red}{+} (5+x) \\\Leftrightarrow & 12x-4& = &-11+5+x \\\Leftrightarrow & 12x \color{red}{-4} & = &-6 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & 12x-x& = &-6+4 \\\Leftrightarrow & 11x& = &-2 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-2}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-2}{11} & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-4x+1)& = & -15 \color{red}{+} (15+x) \\\Leftrightarrow & -8x+2& = &-15+15+x \\\Leftrightarrow & -8x \color{red}{+2} & = &0 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{+2} \color{blue}{-2} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-2} \\\Leftrightarrow & -8x-x& = &0-2 \\\Leftrightarrow & -9x& = &-2 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-2}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{2}{9} & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-2x-6)& = & -6 \color{red}{+} (-14-3x) \\\Leftrightarrow & -4x-12& = &-6-14-3x \\\Leftrightarrow & -4x \color{red}{-12} & = &-20 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-12} \color{blue}{+12} \color{blue}{+3x} & = &-20 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+12} \\\Leftrightarrow & -4x+3x& = &-20+12 \\\Leftrightarrow & -x& = &-8 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-8}{ \color{red}{-1} } \\\Leftrightarrow & x = 8 & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (4x+2)& = & 14 \color{red}{-} (-14+3x) \\\Leftrightarrow & 16x+8& = &14+14-3x \\\Leftrightarrow & 16x \color{red}{+8} & = &28 \color{red}{-3x} \\\Leftrightarrow & 16x \color{red}{+8} \color{blue}{-8} \color{blue}{+3x} & = &28 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-8} \\\Leftrightarrow & 16x+3x& = &28-8 \\\Leftrightarrow & 19x& = &20 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{20}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{20}{19} & & \\ & V = \left\{ \frac{20}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (6x+2)& = & -5 \color{red}{-} (-3+x) \\\Leftrightarrow & 18x+6& = &-5+3-x \\\Leftrightarrow & 18x \color{red}{+6} & = &-2 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 18x+x& = &-2-6 \\\Leftrightarrow & 19x& = &-8 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-8}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-8}{19} & & \\ & V = \left\{ \frac{-8}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (5x-1)& = & 5 \color{red}{+} (-15+x) \\\Leftrightarrow & 20x-4& = &5-15+x \\\Leftrightarrow & 20x \color{red}{-4} & = &-10 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & 20x-x& = &-10+4 \\\Leftrightarrow & 19x& = &-6 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-6}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-6}{19} & & \\ & V = \left\{ \frac{-6}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-2x+1)& = & 14 \color{red}{-} (14-3x) \\\Leftrightarrow & -10x+5& = &14-14+3x \\\Leftrightarrow & -10x \color{red}{+5} & = &0 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+5} \color{blue}{-5} \color{blue}{-3x} & = &0 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-5} \\\Leftrightarrow & -10x-3x& = &0-5 \\\Leftrightarrow & -13x& = &-5 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-5}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{5}{13} & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (6x+6)& = & 4 \color{red}{-} (-6+x) \\\Leftrightarrow & 24x+24& = &4+6-x \\\Leftrightarrow & 24x \color{red}{+24} & = &10 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 24x+x& = &10-24 \\\Leftrightarrow & 25x& = &-14 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-14}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-14}{25} & & \\ & V = \left\{ \frac{-14}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-x+4)& = & 2 \color{red}{-} (7-2x) \\\Leftrightarrow & -5x+20& = &2-7+2x \\\Leftrightarrow & -5x \color{red}{+20} & = &-5 \color{red}{+2x} \\\Leftrightarrow & -5x \color{red}{+20} \color{blue}{-20} \color{blue}{-2x} & = &-5 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-20} \\\Leftrightarrow & -5x-2x& = &-5-20 \\\Leftrightarrow & -7x& = &-25 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-25}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{25}{7} & & \\ & V = \left\{ \frac{25}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-6x+3)& = & 11 \color{red}{+} (-6+x) \\\Leftrightarrow & -30x+15& = &11-6+x \\\Leftrightarrow & -30x \color{red}{+15} & = &5 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & -30x-x& = &5-15 \\\Leftrightarrow & -31x& = &-10 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-10}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{10}{31} & & \\ & V = \left\{ \frac{10}{31} \right\} & \\\end{align}\)