Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{-9}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-9}\color{blue}{+9-x } & = & -4 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -4 \color{blue}{+9} \\\Leftrightarrow &-10x & = &5\\\Leftrightarrow & \color{red}{-10}x & = &5\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{5}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{-13}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-13}\color{blue}{+13-x } & = & 15 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 15 \color{blue}{+13} \\\Leftrightarrow &11x & = &28\\\Leftrightarrow & \color{red}{11}x & = &28\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{28}{11} \\\Leftrightarrow & \color{green}{ x = \frac{28}{11} } & & \\ & V = \left\{ \frac{28}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{+9}& = & 11 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{+9}\color{blue}{-9-9x } & = & 11 \color{red}{ +9x }\color{blue}{-9-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & 11 \color{blue}{-9} \\\Leftrightarrow &-13x & = &2\\\Leftrightarrow & \color{red}{-13}x & = &2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{13} } & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{+7}& = & 12 \color{red}{ +14x } \\\Leftrightarrow & -x \color{red}{+7}\color{blue}{-7-14x } & = & 12 \color{red}{ +14x }\color{blue}{-7-14x } \\\Leftrightarrow & -x \color{blue}{-14x } & = & 12 \color{blue}{-7} \\\Leftrightarrow &-15x & = &5\\\Leftrightarrow & \color{red}{-15}x & = &5\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{5}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{-10}& = & 2 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{-10}\color{blue}{+10-7x } & = & 2 \color{red}{ +7x }\color{blue}{+10-7x } \\\Leftrightarrow & 12x \color{blue}{-7x } & = & 2 \color{blue}{+10} \\\Leftrightarrow &5x & = &12\\\Leftrightarrow & \color{red}{5}x & = &12\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{12}{5} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{-10}& = & -12 \color{red}{ +4x } \\\Leftrightarrow & 9x \color{red}{-10}\color{blue}{+10-4x } & = & -12 \color{red}{ +4x }\color{blue}{+10-4x } \\\Leftrightarrow & 9x \color{blue}{-4x } & = & -12 \color{blue}{+10} \\\Leftrightarrow &5x & = &-2\\\Leftrightarrow & \color{red}{5}x & = &-2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{+10}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+10}\color{blue}{-10-x } & = & -12 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -12 \color{blue}{-10} \\\Leftrightarrow &-15x & = &-22\\\Leftrightarrow & \color{red}{-15}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-22}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{22}{15} } & & \\ & V = \left\{ \frac{22}{15} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{-13}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-13}\color{blue}{+13-x } & = & -3 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -3 \color{blue}{+13} \\\Leftrightarrow &-3x & = &10\\\Leftrightarrow & \color{red}{-3}x & = &10\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{10}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{3} } & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{+1}& = & -6 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{+1}\color{blue}{-1-11x } & = & -6 \color{red}{ +11x }\color{blue}{-1-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & -6 \color{blue}{-1} \\\Leftrightarrow &-16x & = &-7\\\Leftrightarrow & \color{red}{-16}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-7}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{7}{16} } & & \\ & V = \left\{ \frac{7}{16} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{+2}& = & 15 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+2}\color{blue}{-2-7x } & = & 15 \color{red}{ +7x }\color{blue}{-2-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & 15 \color{blue}{-2} \\\Leftrightarrow &3x & = &13\\\Leftrightarrow & \color{red}{3}x & = &13\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{13}{3} \\\Leftrightarrow & \color{green}{ x = \frac{13}{3} } & & \\ & V = \left\{ \frac{13}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 12x \color{red}{-8}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-8}\color{blue}{+8-x } & = & 1 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 1 \color{blue}{+8} \\\Leftrightarrow &11x & = &9\\\Leftrightarrow & \color{red}{11}x & = &9\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{9}{11} \\\Leftrightarrow & \color{green}{ x = \frac{9}{11} } & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{+2}& = & 12 \color{red}{ -6x } \\\Leftrightarrow & x \color{red}{+2}\color{blue}{-2+6x } & = & 12 \color{red}{ -6x }\color{blue}{-2+6x } \\\Leftrightarrow & x \color{blue}{+6x } & = & 12 \color{blue}{-2} \\\Leftrightarrow &7x & = &10\\\Leftrightarrow & \color{red}{7}x & = &10\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{10}{7} \\\Leftrightarrow & \color{green}{ x = \frac{10}{7} } & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)