Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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