Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-2x+5)& = & 1 \color{red}{+} (15+x) \\\Leftrightarrow & -12x+30& = &1+15+x \\\Leftrightarrow & -12x \color{red}{+30} & = &16 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -12x-x& = &16-30 \\\Leftrightarrow & -13x& = &-14 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-14}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{14}{13} & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (6x+4)& = & 13 \color{red}{+} (-3-5x) \\\Leftrightarrow & 18x+12& = &13-3-5x \\\Leftrightarrow & 18x \color{red}{+12} & = &10 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{+12} \color{blue}{-12} \color{blue}{+5x} & = &10 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-12} \\\Leftrightarrow & 18x+5x& = &10-12 \\\Leftrightarrow & 23x& = &-2 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-2}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-2}{23} & & \\ & V = \left\{ \frac{-2}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (6x+5)& = & 12 \color{red}{+} (-9-5x) \\\Leftrightarrow & 18x+15& = &12-9-5x \\\Leftrightarrow & 18x \color{red}{+15} & = &3 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{+15} \color{blue}{-15} \color{blue}{+5x} & = &3 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-15} \\\Leftrightarrow & 18x+5x& = &3-15 \\\Leftrightarrow & 23x& = &-12 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-12}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-12}{23} & & \\ & V = \left\{ \frac{-12}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-6x+1)& = & 1 \color{red}{+} (-7+x) \\\Leftrightarrow & -12x+2& = &1-7+x \\\Leftrightarrow & -12x \color{red}{+2} & = &-6 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+2} \color{blue}{-2} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-2} \\\Leftrightarrow & -12x-x& = &-6-2 \\\Leftrightarrow & -13x& = &-8 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-8}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{8}{13} & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-3x-1)& = & 9 \color{red}{-} (1+x) \\\Leftrightarrow & -6x-2& = &9-1-x \\\Leftrightarrow & -6x \color{red}{-2} & = &8 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & -6x+x& = &8+2 \\\Leftrightarrow & -5x& = &10 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{10}{ \color{red}{-5} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-2x+4)& = & -6 \color{red}{-} (-9+3x) \\\Leftrightarrow & -4x+8& = &-6+9-3x \\\Leftrightarrow & -4x \color{red}{+8} & = &3 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+8} \color{blue}{-8} \color{blue}{+3x} & = &3 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-8} \\\Leftrightarrow & -4x+3x& = &3-8 \\\Leftrightarrow & -x& = &-5 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-5}{ \color{red}{-1} } \\\Leftrightarrow & x = 5 & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-2x+1)& = & -7 \color{red}{+} (-7+x) \\\Leftrightarrow & -10x+5& = &-7-7+x \\\Leftrightarrow & -10x \color{red}{+5} & = &-14 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{+5} \color{blue}{-5} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-5} \\\Leftrightarrow & -10x-x& = &-14-5 \\\Leftrightarrow & -11x& = &-19 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-19}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{19}{11} & & \\ & V = \left\{ \frac{19}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (3x-6)& = & 2 \color{red}{-} (-5+x) \\\Leftrightarrow & 12x-24& = &2+5-x \\\Leftrightarrow & 12x \color{red}{-24} & = &7 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 12x+x& = &7+24 \\\Leftrightarrow & 13x& = &31 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{31}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{31}{13} & & \\ & V = \left\{ \frac{31}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-4x+3)& = & -3 \color{red}{+} (14+x) \\\Leftrightarrow & -12x+9& = &-3+14+x \\\Leftrightarrow & -12x \color{red}{+9} & = &11 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+9} \color{blue}{-9} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{-9} \\\Leftrightarrow & -12x-x& = &11-9 \\\Leftrightarrow & -13x& = &2 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{2}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-2}{13} & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-4x-1)& = & 12 \color{red}{-} (-11+x) \\\Leftrightarrow & -8x-2& = &12+11-x \\\Leftrightarrow & -8x \color{red}{-2} & = &23 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &23 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & -8x+x& = &23+2 \\\Leftrightarrow & -7x& = &25 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{25}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-25}{7} & & \\ & V = \left\{ \frac{-25}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (6x+2)& = & 14 \color{red}{-} (1+x) \\\Leftrightarrow & 24x+8& = &14-1-x \\\Leftrightarrow & 24x \color{red}{+8} & = &13 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 24x+x& = &13-8 \\\Leftrightarrow & 25x& = &5 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{5}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{1}{5} & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-x-7)& = & -7 \color{red}{+} (10-5x) \\\Leftrightarrow & -6x-42& = &-7+10-5x \\\Leftrightarrow & -6x \color{red}{-42} & = &3 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-42} \color{blue}{+42} \color{blue}{+5x} & = &3 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+42} \\\Leftrightarrow & -6x+5x& = &3+42 \\\Leftrightarrow & -x& = &45 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{45}{ \color{red}{-1} } \\\Leftrightarrow & x = -45 & & \\ & V = \left\{ -45 \right\} & \\\end{align}\)