Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{-7}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-7}\color{blue}{+7-x } & = & -12 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -12 \color{blue}{+7} \\\Leftrightarrow &-13x & = &-5\\\Leftrightarrow & \color{red}{-13}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-5}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{5}{13} } & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{+15}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+15}\color{blue}{-15-x } & = & 12 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 12 \color{blue}{-15} \\\Leftrightarrow &-14x & = &-3\\\Leftrightarrow & \color{red}{-14}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-3}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{14} } & & \\ & V = \left\{ \frac{3}{14} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{+13}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+13}\color{blue}{-13-x } & = & 14 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 14 \color{blue}{-13} \\\Leftrightarrow &-10x & = &1\\\Leftrightarrow & \color{red}{-10}x & = &1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{+15}& = & 3 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+15}\color{blue}{-15-7x } & = & 3 \color{red}{ +7x }\color{blue}{-15-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & 3 \color{blue}{-15} \\\Leftrightarrow &3x & = &-12\\\Leftrightarrow & \color{red}{3}x & = &-12\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-12}{3} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{-15}& = & -7 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{-15}\color{blue}{+15-8x } & = & -7 \color{red}{ +8x }\color{blue}{+15-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & -7 \color{blue}{+15} \\\Leftrightarrow &-23x & = &8\\\Leftrightarrow & \color{red}{-23}x & = &8\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{8}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{23} } & & \\ & V = \left\{ \frac{-8}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{-15}& = & -14 \color{red}{ +13x } \\\Leftrightarrow & 9x \color{red}{-15}\color{blue}{+15-13x } & = & -14 \color{red}{ +13x }\color{blue}{+15-13x } \\\Leftrightarrow & 9x \color{blue}{-13x } & = & -14 \color{blue}{+15} \\\Leftrightarrow &-4x & = &1\\\Leftrightarrow & \color{red}{-4}x & = &1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{+9}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+9}\color{blue}{-9-x } & = & -14 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -14 \color{blue}{-9} \\\Leftrightarrow &x & = &-23\\\Leftrightarrow & \color{red}{}x & = &-23\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -23 \\\Leftrightarrow & \color{green}{ x = -23 } & & \\ & V = \left\{ -23 \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{+11}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+11}\color{blue}{-11-x } & = & 3 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 3 \color{blue}{-11} \\\Leftrightarrow &x & = &-8\\\Leftrightarrow & \color{red}{}x & = &-8\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -8 \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
9. \(\begin{align} & x \color{red}{-2}& = & 11 \color{red}{ -x } \\\Leftrightarrow & x \color{red}{-2}\color{blue}{+2+x } & = & 11 \color{red}{ -x }\color{blue}{+2+x } \\\Leftrightarrow & x \color{blue}{+x } & = & 11 \color{blue}{+2} \\\Leftrightarrow &2x & = &13\\\Leftrightarrow & \color{red}{2}x & = &13\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{13}{2} \\\Leftrightarrow & \color{green}{ x = \frac{13}{2} } & & \\ & V = \left\{ \frac{13}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{-7}& = & 4 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{-7}\color{blue}{+7-7x } & = & 4 \color{red}{ +7x }\color{blue}{+7-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & 4 \color{blue}{+7} \\\Leftrightarrow &-5x & = &11\\\Leftrightarrow & \color{red}{-5}x & = &11\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{11}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{5} } & & \\ & V = \left\{ \frac{-11}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{+13}& = & 4 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+13}\color{blue}{-13+2x } & = & 4 \color{red}{ -2x }\color{blue}{-13+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & 4 \color{blue}{-13} \\\Leftrightarrow &17x & = &-9\\\Leftrightarrow & \color{red}{17}x & = &-9\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-9}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{17} } & & \\ & V = \left\{ \frac{-9}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{-13}& = & -9 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-13}\color{blue}{+13+11x } & = & -9 \color{red}{ -11x }\color{blue}{+13+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -9 \color{blue}{+13} \\\Leftrightarrow &23x & = &4\\\Leftrightarrow & \color{red}{23}x & = &4\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{4}{23} \\\Leftrightarrow & \color{green}{ x = \frac{4}{23} } & & \\ & V = \left\{ \frac{4}{23} \right\} & \\\end{align}\)