Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-6x+3)& = & 6 \color{red}{-} (-13+x) \\\Leftrightarrow & -12x+6& = &6+13-x \\\Leftrightarrow & -12x \color{red}{+6} & = &19 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &19 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -12x+x& = &19-6 \\\Leftrightarrow & -11x& = &13 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{13}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-13}{11} & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (2x+2)& = & 4 \color{red}{-} (-9+3x) \\\Leftrightarrow & 8x+8& = &4+9-3x \\\Leftrightarrow & 8x \color{red}{+8} & = &13 \color{red}{-3x} \\\Leftrightarrow & 8x \color{red}{+8} \color{blue}{-8} \color{blue}{+3x} & = &13 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-8} \\\Leftrightarrow & 8x+3x& = &13-8 \\\Leftrightarrow & 11x& = &5 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{5}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{5}{11} & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (2x+6)& = & -7 \color{red}{+} (-15-5x) \\\Leftrightarrow & 6x+18& = &-7-15-5x \\\Leftrightarrow & 6x \color{red}{+18} & = &-22 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+18} \color{blue}{-18} \color{blue}{+5x} & = &-22 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-18} \\\Leftrightarrow & 6x+5x& = &-22-18 \\\Leftrightarrow & 11x& = &-40 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-40}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-40}{11} & & \\ & V = \left\{ \frac{-40}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (x+6)& = & 8 \color{red}{+} (15-5x) \\\Leftrightarrow & 6x+36& = &8+15-5x \\\Leftrightarrow & 6x \color{red}{+36} & = &23 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+36} \color{blue}{-36} \color{blue}{+5x} & = &23 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-36} \\\Leftrightarrow & 6x+5x& = &23-36 \\\Leftrightarrow & 11x& = &-13 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-13}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-13}{11} & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-4x+2)& = & 4 \color{red}{-} (13+x) \\\Leftrightarrow & -20x+10& = &4-13-x \\\Leftrightarrow & -20x \color{red}{+10} & = &-9 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & -20x+x& = &-9-10 \\\Leftrightarrow & -19x& = &-19 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-19}{ \color{red}{-19} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (2x+4)& = & 5 \color{red}{+} (-5+3x) \\\Leftrightarrow & 8x+16& = &5-5+3x \\\Leftrightarrow & 8x \color{red}{+16} & = &0 \color{red}{+3x} \\\Leftrightarrow & 8x \color{red}{+16} \color{blue}{-16} \color{blue}{-3x} & = &0 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-16} \\\Leftrightarrow & 8x-3x& = &0-16 \\\Leftrightarrow & 5x& = &-16 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-16}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-16}{5} & & \\ & V = \left\{ \frac{-16}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (3x+2)& = & -10 \color{red}{-} (-9+4x) \\\Leftrightarrow & 9x+6& = &-10+9-4x \\\Leftrightarrow & 9x \color{red}{+6} & = &-1 \color{red}{-4x} \\\Leftrightarrow & 9x \color{red}{+6} \color{blue}{-6} \color{blue}{+4x} & = &-1 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-6} \\\Leftrightarrow & 9x+4x& = &-1-6 \\\Leftrightarrow & 13x& = &-7 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-7}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-7}{13} & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-2x-3)& = & -7 \color{red}{-} (-13+x) \\\Leftrightarrow & -6x-9& = &-7+13-x \\\Leftrightarrow & -6x \color{red}{-9} & = &6 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-9} \color{blue}{+9} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{+9} \\\Leftrightarrow & -6x+x& = &6+9 \\\Leftrightarrow & -5x& = &15 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{15}{ \color{red}{-5} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-2x-7)& = & -11 \color{red}{+} (11-3x) \\\Leftrightarrow & -10x-35& = &-11+11-3x \\\Leftrightarrow & -10x \color{red}{-35} & = &0 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{-35} \color{blue}{+35} \color{blue}{+3x} & = &0 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+35} \\\Leftrightarrow & -10x+3x& = &0+35 \\\Leftrightarrow & -7x& = &35 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{35}{ \color{red}{-7} } \\\Leftrightarrow & x = -5 & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (5x-1)& = & -14 \color{red}{-} (11+x) \\\Leftrightarrow & 20x-4& = &-14-11-x \\\Leftrightarrow & 20x \color{red}{-4} & = &-25 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-25 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 20x+x& = &-25+4 \\\Leftrightarrow & 21x& = &-21 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-21}{ \color{red}{21} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-6x+5)& = & 4 \color{red}{-} (-7+x) \\\Leftrightarrow & -24x+20& = &4+7-x \\\Leftrightarrow & -24x \color{red}{+20} & = &11 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & -24x+x& = &11-20 \\\Leftrightarrow & -23x& = &-9 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-9}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{9}{23} & & \\ & V = \left\{ \frac{9}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-4x+2)& = & 7 \color{red}{-} (7+x) \\\Leftrightarrow & -24x+12& = &7-7-x \\\Leftrightarrow & -24x \color{red}{+12} & = &0 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -24x+x& = &0-12 \\\Leftrightarrow & -23x& = &-12 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-12}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{12}{23} & & \\ & V = \left\{ \frac{12}{23} \right\} & \\\end{align}\)