Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (4x+2)& = & -1 \color{red}{+} (11+3x) \\\Leftrightarrow & 20x+10& = &-1+11+3x \\\Leftrightarrow & 20x \color{red}{+10} & = &10 \color{red}{+3x} \\\Leftrightarrow & 20x \color{red}{+10} \color{blue}{-10} \color{blue}{-3x} & = &10 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-10} \\\Leftrightarrow & 20x-3x& = &10-10 \\\Leftrightarrow & 17x& = &0 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{0}{ \color{red}{17} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-2x+7)& = & -13 \color{red}{+} (-4+x) \\\Leftrightarrow & -8x+28& = &-13-4+x \\\Leftrightarrow & -8x \color{red}{+28} & = &-17 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & -8x-x& = &-17-28 \\\Leftrightarrow & -9x& = &-45 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-45}{ \color{red}{-9} } \\\Leftrightarrow & x = 5 & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (4x-5)& = & -4 \color{red}{-} (-4+x) \\\Leftrightarrow & 12x-15& = &-4+4-x \\\Leftrightarrow & 12x \color{red}{-15} & = &0 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & 12x+x& = &0+15 \\\Leftrightarrow & 13x& = &15 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{15}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{15}{13} & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-6x-6)& = & -1 \color{red}{+} (-11+x) \\\Leftrightarrow & -24x-24& = &-1-11+x \\\Leftrightarrow & -24x \color{red}{-24} & = &-12 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -24x-x& = &-12+24 \\\Leftrightarrow & -25x& = &12 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{12}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-12}{25} & & \\ & V = \left\{ \frac{-12}{25} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (x+3)& = & -12 \color{red}{-} (-1+x) \\\Leftrightarrow & 6x+18& = &-12+1-x \\\Leftrightarrow & 6x \color{red}{+18} & = &-11 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 6x+x& = &-11-18 \\\Leftrightarrow & 7x& = &-29 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-29}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-29}{7} & & \\ & V = \left\{ \frac{-29}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-6x-1)& = & -11 \color{red}{-} (14+x) \\\Leftrightarrow & -24x-4& = &-11-14-x \\\Leftrightarrow & -24x \color{red}{-4} & = &-25 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-25 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & -24x+x& = &-25+4 \\\Leftrightarrow & -23x& = &-21 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-21}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{21}{23} & & \\ & V = \left\{ \frac{21}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-x-1)& = & -11 \color{red}{-} (10+x) \\\Leftrightarrow & -2x-2& = &-11-10-x \\\Leftrightarrow & -2x \color{red}{-2} & = &-21 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &-21 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & -2x+x& = &-21+2 \\\Leftrightarrow & -x& = &-19 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-19}{ \color{red}{-1} } \\\Leftrightarrow & x = 19 & & \\ & V = \left\{ 19 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (2x+4)& = & -2 \color{red}{+} (11-3x) \\\Leftrightarrow & 10x+20& = &-2+11-3x \\\Leftrightarrow & 10x \color{red}{+20} & = &9 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+20} \color{blue}{-20} \color{blue}{+3x} & = &9 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-20} \\\Leftrightarrow & 10x+3x& = &9-20 \\\Leftrightarrow & 13x& = &-11 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-11}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-11}{13} & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-x+1)& = & -14 \color{red}{-} (9-3x) \\\Leftrightarrow & -4x+4& = &-14-9+3x \\\Leftrightarrow & -4x \color{red}{+4} & = &-23 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+4} \color{blue}{-4} \color{blue}{-3x} & = &-23 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-4} \\\Leftrightarrow & -4x-3x& = &-23-4 \\\Leftrightarrow & -7x& = &-27 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-27}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{27}{7} & & \\ & V = \left\{ \frac{27}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (4x+3)& = & 5 \color{red}{+} (13+x) \\\Leftrightarrow & 20x+15& = &5+13+x \\\Leftrightarrow & 20x \color{red}{+15} & = &18 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &18 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & 20x-x& = &18-15 \\\Leftrightarrow & 19x& = &3 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{3}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{3}{19} & & \\ & V = \left\{ \frac{3}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-4x-3)& = & -8 \color{red}{+} (3-5x) \\\Leftrightarrow & -8x-6& = &-8+3-5x \\\Leftrightarrow & -8x \color{red}{-6} & = &-5 \color{red}{-5x} \\\Leftrightarrow & -8x \color{red}{-6} \color{blue}{+6} \color{blue}{+5x} & = &-5 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+6} \\\Leftrightarrow & -8x+5x& = &-5+6 \\\Leftrightarrow & -3x& = &1 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{1}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-1}{3} & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (3x+3)& = & 5 \color{red}{-} (5-2x) \\\Leftrightarrow & 15x+15& = &5-5+2x \\\Leftrightarrow & 15x \color{red}{+15} & = &0 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+15} \color{blue}{-15} \color{blue}{-2x} & = &0 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-15} \\\Leftrightarrow & 15x-2x& = &0-15 \\\Leftrightarrow & 13x& = &-15 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-15}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-15}{13} & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)