Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-5x+6)& = & 5 \color{red}{+} (-3+x) \\\Leftrightarrow & -20x+24& = &5-3+x \\\Leftrightarrow & -20x \color{red}{+24} & = &2 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -20x-x& = &2-24 \\\Leftrightarrow & -21x& = &-22 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-22}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{22}{21} & & \\ & V = \left\{ \frac{22}{21} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (2x-1)& = & 7 \color{red}{-} (-9-5x) \\\Leftrightarrow & 6x-3& = &7+9+5x \\\Leftrightarrow & 6x \color{red}{-3} & = &16 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-3} \color{blue}{+3} \color{blue}{-5x} & = &16 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+3} \\\Leftrightarrow & 6x-5x& = &16+3 \\\Leftrightarrow & x& = &19 \\ & V = \left\{ 19 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-2x-4)& = & 8 \color{red}{+} (3+x) \\\Leftrightarrow & -10x-20& = &8+3+x \\\Leftrightarrow & -10x \color{red}{-20} & = &11 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & -10x-x& = &11+20 \\\Leftrightarrow & -11x& = &31 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{31}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-31}{11} & & \\ & V = \left\{ \frac{-31}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-4x+5)& = & 13 \color{red}{-} (-12+x) \\\Leftrightarrow & -12x+15& = &13+12-x \\\Leftrightarrow & -12x \color{red}{+15} & = &25 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &25 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & -12x+x& = &25-15 \\\Leftrightarrow & -11x& = &10 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{10}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-10}{11} & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (3x-3)& = & -13 \color{red}{-} (10+x) \\\Leftrightarrow & 12x-12& = &-13-10-x \\\Leftrightarrow & 12x \color{red}{-12} & = &-23 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-23 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 12x+x& = &-23+12 \\\Leftrightarrow & 13x& = &-11 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-11}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-11}{13} & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (x+1)& = & -7 \color{red}{+} (-2-5x) \\\Leftrightarrow & 6x+6& = &-7-2-5x \\\Leftrightarrow & 6x \color{red}{+6} & = &-9 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &-9 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & 6x+5x& = &-9-6 \\\Leftrightarrow & 11x& = &-15 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-15}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-15}{11} & & \\ & V = \left\{ \frac{-15}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-4x+6)& = & -13 \color{red}{-} (-9+x) \\\Leftrightarrow & -16x+24& = &-13+9-x \\\Leftrightarrow & -16x \color{red}{+24} & = &-4 \color{red}{-x} \\\Leftrightarrow & -16x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -16x+x& = &-4-24 \\\Leftrightarrow & -15x& = &-28 \\\Leftrightarrow & \frac{-15x}{ \color{red}{-15} }& = &\frac{-28}{ \color{red}{-15} } \\\Leftrightarrow & x = \frac{28}{15} & & \\ & V = \left\{ \frac{28}{15} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-3x+5)& = & -5 \color{red}{+} (-8-4x) \\\Leftrightarrow & -9x+15& = &-5-8-4x \\\Leftrightarrow & -9x \color{red}{+15} & = &-13 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{+15} \color{blue}{-15} \color{blue}{+4x} & = &-13 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-15} \\\Leftrightarrow & -9x+4x& = &-13-15 \\\Leftrightarrow & -5x& = &-28 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-28}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{28}{5} & & \\ & V = \left\{ \frac{28}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-3x-2)& = & 2 \color{red}{+} (14-2x) \\\Leftrightarrow & -9x-6& = &2+14-2x \\\Leftrightarrow & -9x \color{red}{-6} & = &16 \color{red}{-2x} \\\Leftrightarrow & -9x \color{red}{-6} \color{blue}{+6} \color{blue}{+2x} & = &16 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+6} \\\Leftrightarrow & -9x+2x& = &16+6 \\\Leftrightarrow & -7x& = &22 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{22}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-22}{7} & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (2x+2)& = & -6 \color{red}{+} (7+x) \\\Leftrightarrow & 10x+10& = &-6+7+x \\\Leftrightarrow & 10x \color{red}{+10} & = &1 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & 10x-x& = &1-10 \\\Leftrightarrow & 9x& = &-9 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-9}{ \color{red}{9} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-6x+6)& = & 5 \color{red}{-} (-13+x) \\\Leftrightarrow & -36x+36& = &5+13-x \\\Leftrightarrow & -36x \color{red}{+36} & = &18 \color{red}{-x} \\\Leftrightarrow & -36x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &18 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & -36x+x& = &18-36 \\\Leftrightarrow & -35x& = &-18 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = &\frac{-18}{ \color{red}{-35} } \\\Leftrightarrow & x = \frac{18}{35} & & \\ & V = \left\{ \frac{18}{35} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-3x+2)& = & -14 \color{red}{+} (5-5x) \\\Leftrightarrow & -6x+4& = &-14+5-5x \\\Leftrightarrow & -6x \color{red}{+4} & = &-9 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+4} \color{blue}{-4} \color{blue}{+5x} & = &-9 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-4} \\\Leftrightarrow & -6x+5x& = &-9-4 \\\Leftrightarrow & -x& = &-13 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-13}{ \color{red}{-1} } \\\Leftrightarrow & x = 13 & & \\ & V = \left\{ 13 \right\} & \\\end{align}\)