Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{-6}& = & 8 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{-6}\color{blue}{+6+7x } & = & 8 \color{red}{ -7x }\color{blue}{+6+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & 8 \color{blue}{+6} \\\Leftrightarrow &19x & = &14\\\Leftrightarrow & \color{red}{19}x & = &14\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{14}{19} \\\Leftrightarrow & \color{green}{ x = \frac{14}{19} } & & \\ & V = \left\{ \frac{14}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{+3}& = & -13 \color{red}{ +3x } \\\Leftrightarrow & -11x \color{red}{+3}\color{blue}{-3-3x } & = & -13 \color{red}{ +3x }\color{blue}{-3-3x } \\\Leftrightarrow & -11x \color{blue}{-3x } & = & -13 \color{blue}{-3} \\\Leftrightarrow &-14x & = &-16\\\Leftrightarrow & \color{red}{-14}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-16}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{8}{7} } & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{-8}& = & 10 \color{red}{ -14x } \\\Leftrightarrow & 3x \color{red}{-8}\color{blue}{+8+14x } & = & 10 \color{red}{ -14x }\color{blue}{+8+14x } \\\Leftrightarrow & 3x \color{blue}{+14x } & = & 10 \color{blue}{+8} \\\Leftrightarrow &17x & = &18\\\Leftrightarrow & \color{red}{17}x & = &18\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{18}{17} \\\Leftrightarrow & \color{green}{ x = \frac{18}{17} } & & \\ & V = \left\{ \frac{18}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{-13}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-13}\color{blue}{+13-x } & = & -14 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -14 \color{blue}{+13} \\\Leftrightarrow &x & = &-1\\\Leftrightarrow & \color{red}{}x & = &-1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -1 \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{+13}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+13}\color{blue}{-13-7x } & = & -7 \color{red}{ +7x }\color{blue}{-13-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -7 \color{blue}{-13} \\\Leftrightarrow &-20x & = &-20\\\Leftrightarrow & \color{red}{-20}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-20}{-20} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{-15}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-15}\color{blue}{+15-x } & = & 3 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 3 \color{blue}{+15} \\\Leftrightarrow &-5x & = &18\\\Leftrightarrow & \color{red}{-5}x & = &18\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{18}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{5} } & & \\ & V = \left\{ \frac{-18}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{+5}& = & -7 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{+5}\color{blue}{-5-10x } & = & -7 \color{red}{ +10x }\color{blue}{-5-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & -7 \color{blue}{-5} \\\Leftrightarrow &-13x & = &-12\\\Leftrightarrow & \color{red}{-13}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-12}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{12}{13} } & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{+1}& = & -6 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+1}\color{blue}{-1+7x } & = & -6 \color{red}{ -7x }\color{blue}{-1+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -6 \color{blue}{-1} \\\Leftrightarrow &15x & = &-7\\\Leftrightarrow & \color{red}{15}x & = &-7\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-7}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{15} } & & \\ & V = \left\{ \frac{-7}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{-2}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-2}\color{blue}{+2-x } & = & 14 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 14 \color{blue}{+2} \\\Leftrightarrow &-7x & = &16\\\Leftrightarrow & \color{red}{-7}x & = &16\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{16}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{7} } & & \\ & V = \left\{ \frac{-16}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{+2}& = & 6 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{+2}\color{blue}{-2-10x } & = & 6 \color{red}{ +10x }\color{blue}{-2-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & 6 \color{blue}{-2} \\\Leftrightarrow &-19x & = &4\\\Leftrightarrow & \color{red}{-19}x & = &4\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{4}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{19} } & & \\ & V = \left\{ \frac{-4}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{-13}& = & 3 \color{red}{ +8x } \\\Leftrightarrow & 3x \color{red}{-13}\color{blue}{+13-8x } & = & 3 \color{red}{ +8x }\color{blue}{+13-8x } \\\Leftrightarrow & 3x \color{blue}{-8x } & = & 3 \color{blue}{+13} \\\Leftrightarrow &-5x & = &16\\\Leftrightarrow & \color{red}{-5}x & = &16\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{16}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{5} } & & \\ & V = \left\{ \frac{-16}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{+4}& = & 15 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{+4}\color{blue}{-4-14x } & = & 15 \color{red}{ +14x }\color{blue}{-4-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & 15 \color{blue}{-4} \\\Leftrightarrow &-23x & = &11\\\Leftrightarrow & \color{red}{-23}x & = &11\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{11}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{23} } & & \\ & V = \left\{ \frac{-11}{23} \right\} & \\\end{align}\)