Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-3x+5)& = & -8 \color{red}{+} (-14+x) \\\Leftrightarrow & -12x+20& = &-8-14+x \\\Leftrightarrow & -12x \color{red}{+20} & = &-22 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &-22 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & -12x-x& = &-22-20 \\\Leftrightarrow & -13x& = &-42 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-42}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{42}{13} & & \\ & V = \left\{ \frac{42}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-3x-5)& = & 13 \color{red}{-} (10-5x) \\\Leftrightarrow & -6x-10& = &13-10+5x \\\Leftrightarrow & -6x \color{red}{-10} & = &3 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-10} \color{blue}{+10} \color{blue}{-5x} & = &3 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+10} \\\Leftrightarrow & -6x-5x& = &3+10 \\\Leftrightarrow & -11x& = &13 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{13}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-13}{11} & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-6x+3)& = & -2 \color{red}{-} (-1+x) \\\Leftrightarrow & -24x+12& = &-2+1-x \\\Leftrightarrow & -24x \color{red}{+12} & = &-1 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -24x+x& = &-1-12 \\\Leftrightarrow & -23x& = &-13 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-13}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{13}{23} & & \\ & V = \left\{ \frac{13}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (2x-4)& = & -11 \color{red}{+} (5+3x) \\\Leftrightarrow & 8x-16& = &-11+5+3x \\\Leftrightarrow & 8x \color{red}{-16} & = &-6 \color{red}{+3x} \\\Leftrightarrow & 8x \color{red}{-16} \color{blue}{+16} \color{blue}{-3x} & = &-6 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+16} \\\Leftrightarrow & 8x-3x& = &-6+16 \\\Leftrightarrow & 5x& = &10 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{10}{ \color{red}{5} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (5x-5)& = & 1 \color{red}{+} (-9-3x) \\\Leftrightarrow & 10x-10& = &1-9-3x \\\Leftrightarrow & 10x \color{red}{-10} & = &-8 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-10} \color{blue}{+10} \color{blue}{+3x} & = &-8 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+10} \\\Leftrightarrow & 10x+3x& = &-8+10 \\\Leftrightarrow & 13x& = &2 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{2}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{2}{13} & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (x+2)& = & -11 \color{red}{-} (15-4x) \\\Leftrightarrow & 5x+10& = &-11-15+4x \\\Leftrightarrow & 5x \color{red}{+10} & = &-26 \color{red}{+4x} \\\Leftrightarrow & 5x \color{red}{+10} \color{blue}{-10} \color{blue}{-4x} & = &-26 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-10} \\\Leftrightarrow & 5x-4x& = &-26-10 \\\Leftrightarrow & x& = &-36 \\ & V = \left\{ -36 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-6x+5)& = & -15 \color{red}{-} (-3+x) \\\Leftrightarrow & -18x+15& = &-15+3-x \\\Leftrightarrow & -18x \color{red}{+15} & = &-12 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & -18x+x& = &-12-15 \\\Leftrightarrow & -17x& = &-27 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-27}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{27}{17} & & \\ & V = \left\{ \frac{27}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-5x+3)& = & 9 \color{red}{+} (6+x) \\\Leftrightarrow & -30x+18& = &9+6+x \\\Leftrightarrow & -30x \color{red}{+18} & = &15 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & -30x-x& = &15-18 \\\Leftrightarrow & -31x& = &-3 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-3}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{3}{31} & & \\ & V = \left\{ \frac{3}{31} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (x-6)& = & -12 \color{red}{-} (-3-4x) \\\Leftrightarrow & 5x-30& = &-12+3+4x \\\Leftrightarrow & 5x \color{red}{-30} & = &-9 \color{red}{+4x} \\\Leftrightarrow & 5x \color{red}{-30} \color{blue}{+30} \color{blue}{-4x} & = &-9 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+30} \\\Leftrightarrow & 5x-4x& = &-9+30 \\\Leftrightarrow & x& = &21 \\ & V = \left\{ 21 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (x-5)& = & -3 \color{red}{+} (14-4x) \\\Leftrightarrow & 5x-25& = &-3+14-4x \\\Leftrightarrow & 5x \color{red}{-25} & = &11 \color{red}{-4x} \\\Leftrightarrow & 5x \color{red}{-25} \color{blue}{+25} \color{blue}{+4x} & = &11 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+25} \\\Leftrightarrow & 5x+4x& = &11+25 \\\Leftrightarrow & 9x& = &36 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{36}{ \color{red}{9} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (3x+6)& = & 15 \color{red}{+} (11+x) \\\Leftrightarrow & 18x+36& = &15+11+x \\\Leftrightarrow & 18x \color{red}{+36} & = &26 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &26 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & 18x-x& = &26-36 \\\Leftrightarrow & 17x& = &-10 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-10}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-10}{17} & & \\ & V = \left\{ \frac{-10}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-x+2)& = & 12 \color{red}{-} (-7-5x) \\\Leftrightarrow & -6x+12& = &12+7+5x \\\Leftrightarrow & -6x \color{red}{+12} & = &19 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &19 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & -6x-5x& = &19-12 \\\Leftrightarrow & -11x& = &7 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{7}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-7}{11} & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)