Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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