Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{-1}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-1}\color{blue}{+1-x } & = & 5 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 5 \color{blue}{+1} \\\Leftrightarrow &-12x & = &6\\\Leftrightarrow & \color{red}{-12}x & = &6\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{6}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{+11}& = & -11 \color{red}{ +10x } \\\Leftrightarrow & 7x \color{red}{+11}\color{blue}{-11-10x } & = & -11 \color{red}{ +10x }\color{blue}{-11-10x } \\\Leftrightarrow & 7x \color{blue}{-10x } & = & -11 \color{blue}{-11} \\\Leftrightarrow &-3x & = &-22\\\Leftrightarrow & \color{red}{-3}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-22}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{22}{3} } & & \\ & V = \left\{ \frac{22}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{-5}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-5}\color{blue}{+5-x } & = & 3 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 3 \color{blue}{+5} \\\Leftrightarrow &-12x & = &8\\\Leftrightarrow & \color{red}{-12}x & = &8\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{8}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{-10}& = & 11 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{-10}\color{blue}{+10-5x } & = & 11 \color{red}{ +5x }\color{blue}{+10-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & 11 \color{blue}{+10} \\\Leftrightarrow &7x & = &21\\\Leftrightarrow & \color{red}{7}x & = &21\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{21}{7} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{+9}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+9}\color{blue}{-9-x } & = & 6 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 6 \color{blue}{-9} \\\Leftrightarrow &x & = &-3\\\Leftrightarrow & \color{red}{}x & = &-3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -3 \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{-13}& = & -4 \color{red}{ +14x } \\\Leftrightarrow & 3x \color{red}{-13}\color{blue}{+13-14x } & = & -4 \color{red}{ +14x }\color{blue}{+13-14x } \\\Leftrightarrow & 3x \color{blue}{-14x } & = & -4 \color{blue}{+13} \\\Leftrightarrow &-11x & = &9\\\Leftrightarrow & \color{red}{-11}x & = &9\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{9}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{11} } & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{-10}& = & -1 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-10}\color{blue}{+10+7x } & = & -1 \color{red}{ -7x }\color{blue}{+10+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -1 \color{blue}{+10} \\\Leftrightarrow &15x & = &9\\\Leftrightarrow & \color{red}{15}x & = &9\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{9}{15} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{+3}& = & 15 \color{red}{ +8x } \\\Leftrightarrow & 13x \color{red}{+3}\color{blue}{-3-8x } & = & 15 \color{red}{ +8x }\color{blue}{-3-8x } \\\Leftrightarrow & 13x \color{blue}{-8x } & = & 15 \color{blue}{-3} \\\Leftrightarrow &5x & = &12\\\Leftrightarrow & \color{red}{5}x & = &12\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{12}{5} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{-8}& = & -1 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{-8}\color{blue}{+8+13x } & = & -1 \color{red}{ -13x }\color{blue}{+8+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & -1 \color{blue}{+8} \\\Leftrightarrow &20x & = &7\\\Leftrightarrow & \color{red}{20}x & = &7\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{7}{20} \\\Leftrightarrow & \color{green}{ x = \frac{7}{20} } & & \\ & V = \left\{ \frac{7}{20} \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{+8}& = & -8 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{+8}\color{blue}{-8-7x } & = & -8 \color{red}{ +7x }\color{blue}{-8-7x } \\\Leftrightarrow & -3x \color{blue}{-7x } & = & -8 \color{blue}{-8} \\\Leftrightarrow &-10x & = &-16\\\Leftrightarrow & \color{red}{-10}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-16}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{+13}& = & -11 \color{red}{ -10x } \\\Leftrightarrow & x \color{red}{+13}\color{blue}{-13+10x } & = & -11 \color{red}{ -10x }\color{blue}{-13+10x } \\\Leftrightarrow & x \color{blue}{+10x } & = & -11 \color{blue}{-13} \\\Leftrightarrow &11x & = &-24\\\Leftrightarrow & \color{red}{11}x & = &-24\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-24}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{11} } & & \\ & V = \left\{ \frac{-24}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{-13}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-13}\color{blue}{+13-x } & = & -8 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -8 \color{blue}{+13} \\\Leftrightarrow &-8x & = &5\\\Leftrightarrow & \color{red}{-8}x & = &5\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{5}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{8} } & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)