Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-6x-3)& = & 14 \color{red}{-} (10-5x) \\\Leftrightarrow & -36x-18& = &14-10+5x \\\Leftrightarrow & -36x \color{red}{-18} & = &4 \color{red}{+5x} \\\Leftrightarrow & -36x \color{red}{-18} \color{blue}{+18} \color{blue}{-5x} & = &4 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+18} \\\Leftrightarrow & -36x-5x& = &4+18 \\\Leftrightarrow & -41x& = &22 \\\Leftrightarrow & \frac{-41x}{ \color{red}{-41} }& = &\frac{22}{ \color{red}{-41} } \\\Leftrightarrow & x = \frac{-22}{41} & & \\ & V = \left\{ \frac{-22}{41} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (2x-2)& = & -10 \color{red}{-} (13+x) \\\Leftrightarrow & 8x-8& = &-10-13-x \\\Leftrightarrow & 8x \color{red}{-8} & = &-23 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &-23 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 8x+x& = &-23+8 \\\Leftrightarrow & 9x& = &-15 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-15}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-5}{3} & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-4x-4)& = & 14 \color{red}{+} (-12+x) \\\Leftrightarrow & -8x-8& = &14-12+x \\\Leftrightarrow & -8x \color{red}{-8} & = &2 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -8x-x& = &2+8 \\\Leftrightarrow & -9x& = &10 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{10}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-10}{9} & & \\ & V = \left\{ \frac{-10}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-6x+4)& = & 3 \color{red}{-} (-11+x) \\\Leftrightarrow & -24x+16& = &3+11-x \\\Leftrightarrow & -24x \color{red}{+16} & = &14 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & -24x+x& = &14-16 \\\Leftrightarrow & -23x& = &-2 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-2}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{2}{23} & & \\ & V = \left\{ \frac{2}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-2x-6)& = & 12 \color{red}{+} (-11-3x) \\\Leftrightarrow & -10x-30& = &12-11-3x \\\Leftrightarrow & -10x \color{red}{-30} & = &1 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{-30} \color{blue}{+30} \color{blue}{+3x} & = &1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+30} \\\Leftrightarrow & -10x+3x& = &1+30 \\\Leftrightarrow & -7x& = &31 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{31}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-31}{7} & & \\ & V = \left\{ \frac{-31}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-4x+3)& = & 11 \color{red}{+} (10+x) \\\Leftrightarrow & -20x+15& = &11+10+x \\\Leftrightarrow & -20x \color{red}{+15} & = &21 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &21 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & -20x-x& = &21-15 \\\Leftrightarrow & -21x& = &6 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{6}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-2}{7} & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-2x+1)& = & 13 \color{red}{-} (2+x) \\\Leftrightarrow & -4x+2& = &13-2-x \\\Leftrightarrow & -4x \color{red}{+2} & = &11 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{+2} \color{blue}{-2} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{-2} \\\Leftrightarrow & -4x+x& = &11-2 \\\Leftrightarrow & -3x& = &9 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{9}{ \color{red}{-3} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-6x-5)& = & -4 \color{red}{-} (8+x) \\\Leftrightarrow & -24x-20& = &-4-8-x \\\Leftrightarrow & -24x \color{red}{-20} & = &-12 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & -24x+x& = &-12+20 \\\Leftrightarrow & -23x& = &8 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{8}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-8}{23} & & \\ & V = \left\{ \frac{-8}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (x-4)& = & -5 \color{red}{+} (7+3x) \\\Leftrightarrow & 5x-20& = &-5+7+3x \\\Leftrightarrow & 5x \color{red}{-20} & = &2 \color{red}{+3x} \\\Leftrightarrow & 5x \color{red}{-20} \color{blue}{+20} \color{blue}{-3x} & = &2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+20} \\\Leftrightarrow & 5x-3x& = &2+20 \\\Leftrightarrow & 2x& = &22 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{22}{ \color{red}{2} } \\\Leftrightarrow & x = 11 & & \\ & V = \left\{ 11 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (6x-3)& = & -7 \color{red}{-} (-4+x) \\\Leftrightarrow & 12x-6& = &-7+4-x \\\Leftrightarrow & 12x \color{red}{-6} & = &-3 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 12x+x& = &-3+6 \\\Leftrightarrow & 13x& = &3 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{3}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{3}{13} & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (3x+4)& = & 8 \color{red}{+} (-1-5x) \\\Leftrightarrow & 6x+8& = &8-1-5x \\\Leftrightarrow & 6x \color{red}{+8} & = &7 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+8} \color{blue}{-8} \color{blue}{+5x} & = &7 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-8} \\\Leftrightarrow & 6x+5x& = &7-8 \\\Leftrightarrow & 11x& = &-1 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-1}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-1}{11} & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (5x+7)& = & -7 \color{red}{-} (3+3x) \\\Leftrightarrow & 25x+35& = &-7-3-3x \\\Leftrightarrow & 25x \color{red}{+35} & = &-10 \color{red}{-3x} \\\Leftrightarrow & 25x \color{red}{+35} \color{blue}{-35} \color{blue}{+3x} & = &-10 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-35} \\\Leftrightarrow & 25x+3x& = &-10-35 \\\Leftrightarrow & 28x& = &-45 \\\Leftrightarrow & \frac{28x}{ \color{red}{28} }& = &\frac{-45}{ \color{red}{28} } \\\Leftrightarrow & x = \frac{-45}{28} & & \\ & V = \left\{ \frac{-45}{28} \right\} & \\\end{align}\)