Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{-15}& = & -1 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{-15}\color{blue}{+15-9x } & = & -1 \color{red}{ +9x }\color{blue}{+15-9x } \\\Leftrightarrow & -11x \color{blue}{-9x } & = & -1 \color{blue}{+15} \\\Leftrightarrow &-20x & = &14\\\Leftrightarrow & \color{red}{-20}x & = &14\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{14}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{10} } & & \\ & V = \left\{ \frac{-7}{10} \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{-10}& = & 11 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{-10}\color{blue}{+10-7x } & = & 11 \color{red}{ +7x }\color{blue}{+10-7x } \\\Leftrightarrow & -3x \color{blue}{-7x } & = & 11 \color{blue}{+10} \\\Leftrightarrow &-10x & = &21\\\Leftrightarrow & \color{red}{-10}x & = &21\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{21}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{10} } & & \\ & V = \left\{ \frac{-21}{10} \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{-3}& = & -11 \color{red}{ +8x } \\\Leftrightarrow & 5x \color{red}{-3}\color{blue}{+3-8x } & = & -11 \color{red}{ +8x }\color{blue}{+3-8x } \\\Leftrightarrow & 5x \color{blue}{-8x } & = & -11 \color{blue}{+3} \\\Leftrightarrow &-3x & = &-8\\\Leftrightarrow & \color{red}{-3}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-8}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{+4}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+4}\color{blue}{-4-x } & = & -2 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -2 \color{blue}{-4} \\\Leftrightarrow &-6x & = &-6\\\Leftrightarrow & \color{red}{-6}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-6}{-6} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{-7}& = & -15 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-7}\color{blue}{+7-7x } & = & -15 \color{red}{ +7x }\color{blue}{+7-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -15 \color{blue}{+7} \\\Leftrightarrow &-20x & = &-8\\\Leftrightarrow & \color{red}{-20}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-8}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{+3}& = & 12 \color{red}{ +5x } \\\Leftrightarrow & 11x \color{red}{+3}\color{blue}{-3-5x } & = & 12 \color{red}{ +5x }\color{blue}{-3-5x } \\\Leftrightarrow & 11x \color{blue}{-5x } & = & 12 \color{blue}{-3} \\\Leftrightarrow &6x & = &9\\\Leftrightarrow & \color{red}{6}x & = &9\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{9}{6} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{+1}& = & 1 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{+1}\color{blue}{-1+11x } & = & 1 \color{red}{ -11x }\color{blue}{-1+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & 1 \color{blue}{-1} \\\Leftrightarrow &15x & = &0\\\Leftrightarrow & \color{red}{15}x & = &0\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{0}{15} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{+9}& = & -4 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+9}\color{blue}{-9-7x } & = & -4 \color{red}{ +7x }\color{blue}{-9-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & -4 \color{blue}{-9} \\\Leftrightarrow &3x & = &-13\\\Leftrightarrow & \color{red}{3}x & = &-13\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-13}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{3} } & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{+13}& = & -3 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{+13}\color{blue}{-13+14x } & = & -3 \color{red}{ -14x }\color{blue}{-13+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & -3 \color{blue}{-13} \\\Leftrightarrow &29x & = &-16\\\Leftrightarrow & \color{red}{29}x & = &-16\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{-16}{29} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{29} } & & \\ & V = \left\{ \frac{-16}{29} \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{-15}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{-15}\color{blue}{+15-x } & = & 6 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & 6 \color{blue}{+15} \\\Leftrightarrow &2x & = &21\\\Leftrightarrow & \color{red}{2}x & = &21\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{21}{2} \\\Leftrightarrow & \color{green}{ x = \frac{21}{2} } & & \\ & V = \left\{ \frac{21}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{-4}& = & -9 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{-4}\color{blue}{+4-8x } & = & -9 \color{red}{ +8x }\color{blue}{+4-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & -9 \color{blue}{+4} \\\Leftrightarrow &-23x & = &-5\\\Leftrightarrow & \color{red}{-23}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-5}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{5}{23} } & & \\ & V = \left\{ \frac{5}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{-14}& = & 13 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{-14}\color{blue}{+14-5x } & = & 13 \color{red}{ +5x }\color{blue}{+14-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & 13 \color{blue}{+14} \\\Leftrightarrow &7x & = &27\\\Leftrightarrow & \color{red}{7}x & = &27\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{27}{7} \\\Leftrightarrow & \color{green}{ x = \frac{27}{7} } & & \\ & V = \left\{ \frac{27}{7} \right\} & \\\end{align}\)