Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{-15}& = & -11 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-15}\color{blue}{+15+13x } & = & -11 \color{red}{ -13x }\color{blue}{+15+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & -11 \color{blue}{+15} \\\Leftrightarrow &23x & = &4\\\Leftrightarrow & \color{red}{23}x & = &4\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{4}{23} \\\Leftrightarrow & \color{green}{ x = \frac{4}{23} } & & \\ & V = \left\{ \frac{4}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{+3}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+3}\color{blue}{-3-x } & = & -15 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -15 \color{blue}{-3} \\\Leftrightarrow &-10x & = &-18\\\Leftrightarrow & \color{red}{-10}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-18}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{+15}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 15x \color{red}{+15}\color{blue}{-15-x } & = & -6 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 15x \color{blue}{-x } & = & -6 \color{blue}{-15} \\\Leftrightarrow &14x & = &-21\\\Leftrightarrow & \color{red}{14}x & = &-21\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-21}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{+4}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+4}\color{blue}{-4-x } & = & -3 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -3 \color{blue}{-4} \\\Leftrightarrow &-16x & = &-7\\\Leftrightarrow & \color{red}{-16}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-7}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{7}{16} } & & \\ & V = \left\{ \frac{7}{16} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{+8}& = & -11 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{+8}\color{blue}{-8+15x } & = & -11 \color{red}{ -15x }\color{blue}{-8+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & -11 \color{blue}{-8} \\\Leftrightarrow &19x & = &-19\\\Leftrightarrow & \color{red}{19}x & = &-19\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-19}{19} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{+1}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+1}\color{blue}{-1-x } & = & 14 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 14 \color{blue}{-1} \\\Leftrightarrow &-15x & = &13\\\Leftrightarrow & \color{red}{-15}x & = &13\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{13}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{15} } & & \\ & V = \left\{ \frac{-13}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{-3}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-3}\color{blue}{+3-x } & = & -8 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -8 \color{blue}{+3} \\\Leftrightarrow &-12x & = &-5\\\Leftrightarrow & \color{red}{-12}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-5}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{12} } & & \\ & V = \left\{ \frac{5}{12} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{-10}& = & -8 \color{red}{ +12x } \\\Leftrightarrow & -7x \color{red}{-10}\color{blue}{+10-12x } & = & -8 \color{red}{ +12x }\color{blue}{+10-12x } \\\Leftrightarrow & -7x \color{blue}{-12x } & = & -8 \color{blue}{+10} \\\Leftrightarrow &-19x & = &2\\\Leftrightarrow & \color{red}{-19}x & = &2\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{2}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{19} } & & \\ & V = \left\{ \frac{-2}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{+9}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+9}\color{blue}{-9-x } & = & 4 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 4 \color{blue}{-9} \\\Leftrightarrow &-16x & = &-5\\\Leftrightarrow & \color{red}{-16}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-5}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{16} } & & \\ & V = \left\{ \frac{5}{16} \right\} & \\\end{align}\)
10. \(\begin{align} & 15x \color{red}{+13}& = & -10 \color{red}{ +4x } \\\Leftrightarrow & 15x \color{red}{+13}\color{blue}{-13-4x } & = & -10 \color{red}{ +4x }\color{blue}{-13-4x } \\\Leftrightarrow & 15x \color{blue}{-4x } & = & -10 \color{blue}{-13} \\\Leftrightarrow &11x & = &-23\\\Leftrightarrow & \color{red}{11}x & = &-23\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-23}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{11} } & & \\ & V = \left\{ \frac{-23}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{-1}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-1}\color{blue}{+1-x } & = & 10 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 10 \color{blue}{+1} \\\Leftrightarrow &13x & = &11\\\Leftrightarrow & \color{red}{13}x & = &11\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{11}{13} \\\Leftrightarrow & \color{green}{ x = \frac{11}{13} } & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{-3}& = & -8 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{-3}\color{blue}{+3-14x } & = & -8 \color{red}{ +14x }\color{blue}{+3-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & -8 \color{blue}{+3} \\\Leftrightarrow &-27x & = &-5\\\Leftrightarrow & \color{red}{-27}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{-5}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{5}{27} } & & \\ & V = \left\{ \frac{5}{27} \right\} & \\\end{align}\)