Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (3x-6)& = & 3 \color{red}{+} (-14-2x) \\\Leftrightarrow & 15x-30& = &3-14-2x \\\Leftrightarrow & 15x \color{red}{-30} & = &-11 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-30} \color{blue}{+30} \color{blue}{+2x} & = &-11 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+30} \\\Leftrightarrow & 15x+2x& = &-11+30 \\\Leftrightarrow & 17x& = &19 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{19}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{19}{17} & & \\ & V = \left\{ \frac{19}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (6x+6)& = & 15 \color{red}{+} (3-5x) \\\Leftrightarrow & 18x+18& = &15+3-5x \\\Leftrightarrow & 18x \color{red}{+18} & = &18 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{+18} \color{blue}{-18} \color{blue}{+5x} & = &18 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-18} \\\Leftrightarrow & 18x+5x& = &18-18 \\\Leftrightarrow & 23x& = &0 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{0}{ \color{red}{23} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-5x+3)& = & -1 \color{red}{+} (15+4x) \\\Leftrightarrow & -25x+15& = &-1+15+4x \\\Leftrightarrow & -25x \color{red}{+15} & = &14 \color{red}{+4x} \\\Leftrightarrow & -25x \color{red}{+15} \color{blue}{-15} \color{blue}{-4x} & = &14 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-15} \\\Leftrightarrow & -25x-4x& = &14-15 \\\Leftrightarrow & -29x& = &-1 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-1}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{1}{29} & & \\ & V = \left\{ \frac{1}{29} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (4x-1)& = & 2 \color{red}{-} (-3+x) \\\Leftrightarrow & 12x-3& = &2+3-x \\\Leftrightarrow & 12x \color{red}{-3} & = &5 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-3} \color{blue}{+3} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{+3} \\\Leftrightarrow & 12x+x& = &5+3 \\\Leftrightarrow & 13x& = &8 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{8}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{8}{13} & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (x+6)& = & 15 \color{red}{-} (-6-5x) \\\Leftrightarrow & 6x+36& = &15+6+5x \\\Leftrightarrow & 6x \color{red}{+36} & = &21 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+36} \color{blue}{-36} \color{blue}{-5x} & = &21 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-36} \\\Leftrightarrow & 6x-5x& = &21-36 \\\Leftrightarrow & x& = &-15 \\ & V = \left\{ -15 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-3x-5)& = & -8 \color{red}{+} (-14+2x) \\\Leftrightarrow & -15x-25& = &-8-14+2x \\\Leftrightarrow & -15x \color{red}{-25} & = &-22 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{-25} \color{blue}{+25} \color{blue}{-2x} & = &-22 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+25} \\\Leftrightarrow & -15x-2x& = &-22+25 \\\Leftrightarrow & -17x& = &3 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{3}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-3}{17} & & \\ & V = \left\{ \frac{-3}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-4x-3)& = & 13 \color{red}{-} (-12+x) \\\Leftrightarrow & -8x-6& = &13+12-x \\\Leftrightarrow & -8x \color{red}{-6} & = &25 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &25 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -8x+x& = &25+6 \\\Leftrightarrow & -7x& = &31 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{31}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-31}{7} & & \\ & V = \left\{ \frac{-31}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-2x+7)& = & -2 \color{red}{-} (-6-3x) \\\Leftrightarrow & -10x+35& = &-2+6+3x \\\Leftrightarrow & -10x \color{red}{+35} & = &4 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+35} \color{blue}{-35} \color{blue}{-3x} & = &4 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-35} \\\Leftrightarrow & -10x-3x& = &4-35 \\\Leftrightarrow & -13x& = &-31 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-31}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{31}{13} & & \\ & V = \left\{ \frac{31}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (5x+3)& = & 2 \color{red}{+} (-6+x) \\\Leftrightarrow & 20x+12& = &2-6+x \\\Leftrightarrow & 20x \color{red}{+12} & = &-4 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 20x-x& = &-4-12 \\\Leftrightarrow & 19x& = &-16 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-16}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-16}{19} & & \\ & V = \left\{ \frac{-16}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-2x+2)& = & -6 \color{red}{+} (-15+x) \\\Leftrightarrow & -8x+8& = &-6-15+x \\\Leftrightarrow & -8x \color{red}{+8} & = &-21 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-21 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -8x-x& = &-21-8 \\\Leftrightarrow & -9x& = &-29 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-29}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{29}{9} & & \\ & V = \left\{ \frac{29}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (6x+3)& = & -9 \color{red}{-} (-9+x) \\\Leftrightarrow & 18x+9& = &-9+9-x \\\Leftrightarrow & 18x \color{red}{+9} & = &0 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+9} \color{blue}{-9} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-9} \\\Leftrightarrow & 18x+x& = &0-9 \\\Leftrightarrow & 19x& = &-9 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-9}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-9}{19} & & \\ & V = \left\{ \frac{-9}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-x-3)& = & 11 \color{red}{-} (-6+x) \\\Leftrightarrow & -5x-15& = &11+6-x \\\Leftrightarrow & -5x \color{red}{-15} & = &17 \color{red}{-x} \\\Leftrightarrow & -5x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & -5x+x& = &17+15 \\\Leftrightarrow & -4x& = &32 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{32}{ \color{red}{-4} } \\\Leftrightarrow & x = -8 & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)