Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{+15}& = & -5 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+15}\color{blue}{-15+11x } & = & -5 \color{red}{ -11x }\color{blue}{-15+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -5 \color{blue}{-15} \\\Leftrightarrow &23x & = &-20\\\Leftrightarrow & \color{red}{23}x & = &-20\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-20}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{23} } & & \\ & V = \left\{ \frac{-20}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{+2}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{+2}\color{blue}{-2-x } & = & -9 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 11x \color{blue}{-x } & = & -9 \color{blue}{-2} \\\Leftrightarrow &10x & = &-11\\\Leftrightarrow & \color{red}{10}x & = &-11\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-11}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{10} } & & \\ & V = \left\{ \frac{-11}{10} \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{+10}& = & -15 \color{red}{ +7x } \\\Leftrightarrow & 5x \color{red}{+10}\color{blue}{-10-7x } & = & -15 \color{red}{ +7x }\color{blue}{-10-7x } \\\Leftrightarrow & 5x \color{blue}{-7x } & = & -15 \color{blue}{-10} \\\Leftrightarrow &-2x & = &-25\\\Leftrightarrow & \color{red}{-2}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-25}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{25}{2} } & & \\ & V = \left\{ \frac{25}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{-15}& = & -3 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{-15}\color{blue}{+15+7x } & = & -3 \color{red}{ -7x }\color{blue}{+15+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & -3 \color{blue}{+15} \\\Leftrightarrow &22x & = &12\\\Leftrightarrow & \color{red}{22}x & = &12\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{12}{22} \\\Leftrightarrow & \color{green}{ x = \frac{6}{11} } & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{-9}& = & 14 \color{red}{ +5x } \\\Leftrightarrow & 2x \color{red}{-9}\color{blue}{+9-5x } & = & 14 \color{red}{ +5x }\color{blue}{+9-5x } \\\Leftrightarrow & 2x \color{blue}{-5x } & = & 14 \color{blue}{+9} \\\Leftrightarrow &-3x & = &23\\\Leftrightarrow & \color{red}{-3}x & = &23\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{23}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{3} } & & \\ & V = \left\{ \frac{-23}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{+11}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+11}\color{blue}{-11-x } & = & 8 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 8 \color{blue}{-11} \\\Leftrightarrow &-3x & = &-3\\\Leftrightarrow & \color{red}{-3}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-3}{-3} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{+12}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+12}\color{blue}{-12-x } & = & -14 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -14 \color{blue}{-12} \\\Leftrightarrow &-6x & = &-26\\\Leftrightarrow & \color{red}{-6}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-26}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{13}{3} } & & \\ & V = \left\{ \frac{13}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{-7}& = & -11 \color{red}{ +5x } \\\Leftrightarrow & 8x \color{red}{-7}\color{blue}{+7-5x } & = & -11 \color{red}{ +5x }\color{blue}{+7-5x } \\\Leftrightarrow & 8x \color{blue}{-5x } & = & -11 \color{blue}{+7} \\\Leftrightarrow &3x & = &-4\\\Leftrightarrow & \color{red}{3}x & = &-4\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-4}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{+9}& = & -11 \color{red}{ +9x } \\\Leftrightarrow & 7x \color{red}{+9}\color{blue}{-9-9x } & = & -11 \color{red}{ +9x }\color{blue}{-9-9x } \\\Leftrightarrow & 7x \color{blue}{-9x } & = & -11 \color{blue}{-9} \\\Leftrightarrow &-2x & = &-20\\\Leftrightarrow & \color{red}{-2}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-20}{-2} \\\Leftrightarrow & \color{green}{ x = 10 } & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{-11}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-11}\color{blue}{+11-x } & = & 9 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 9 \color{blue}{+11} \\\Leftrightarrow &-6x & = &20\\\Leftrightarrow & \color{red}{-6}x & = &20\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{20}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{3} } & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{+12}& = & 6 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+12}\color{blue}{-12+3x } & = & 6 \color{red}{ -3x }\color{blue}{-12+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 6 \color{blue}{-12} \\\Leftrightarrow &13x & = &-6\\\Leftrightarrow & \color{red}{13}x & = &-6\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-6}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{13} } & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{-1}& = & 11 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{-1}\color{blue}{+1+13x } & = & 11 \color{red}{ -13x }\color{blue}{+1+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & 11 \color{blue}{+1} \\\Leftrightarrow &22x & = &12\\\Leftrightarrow & \color{red}{22}x & = &12\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{12}{22} \\\Leftrightarrow & \color{green}{ x = \frac{6}{11} } & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)