Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{-15}& = & 11 \color{red}{ +12x } \\\Leftrightarrow & -x \color{red}{-15}\color{blue}{+15-12x } & = & 11 \color{red}{ +12x }\color{blue}{+15-12x } \\\Leftrightarrow & -x \color{blue}{-12x } & = & 11 \color{blue}{+15} \\\Leftrightarrow &-13x & = &26\\\Leftrightarrow & \color{red}{-13}x & = &26\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{26}{-13} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{-1}& = & 15 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{-1}\color{blue}{+1-4x } & = & 15 \color{red}{ +4x }\color{blue}{+1-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & 15 \color{blue}{+1} \\\Leftrightarrow &-19x & = &16\\\Leftrightarrow & \color{red}{-19}x & = &16\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{16}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{19} } & & \\ & V = \left\{ \frac{-16}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{+8}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+8}\color{blue}{-8-x } & = & 2 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 2 \color{blue}{-8} \\\Leftrightarrow &-14x & = &-6\\\Leftrightarrow & \color{red}{-14}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-6}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{-10}& = & -7 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{-10}\color{blue}{+10-14x } & = & -7 \color{red}{ +14x }\color{blue}{+10-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & -7 \color{blue}{+10} \\\Leftrightarrow &-25x & = &3\\\Leftrightarrow & \color{red}{-25}x & = &3\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{3}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{25} } & & \\ & V = \left\{ \frac{-3}{25} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{-2}& = & 14 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{-2}\color{blue}{+2+11x } & = & 14 \color{red}{ -11x }\color{blue}{+2+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & 14 \color{blue}{+2} \\\Leftrightarrow &15x & = &16\\\Leftrightarrow & \color{red}{15}x & = &16\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{16}{15} \\\Leftrightarrow & \color{green}{ x = \frac{16}{15} } & & \\ & V = \left\{ \frac{16}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{-3}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-3}\color{blue}{+3-x } & = & 10 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 10 \color{blue}{+3} \\\Leftrightarrow &-15x & = &13\\\Leftrightarrow & \color{red}{-15}x & = &13\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{13}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{15} } & & \\ & V = \left\{ \frac{-13}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{+8}& = & 1 \color{red}{ +5x } \\\Leftrightarrow & 2x \color{red}{+8}\color{blue}{-8-5x } & = & 1 \color{red}{ +5x }\color{blue}{-8-5x } \\\Leftrightarrow & 2x \color{blue}{-5x } & = & 1 \color{blue}{-8} \\\Leftrightarrow &-3x & = &-7\\\Leftrightarrow & \color{red}{-3}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-7}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{-15}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-15}\color{blue}{+15-x } & = & 15 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 15 \color{blue}{+15} \\\Leftrightarrow &-3x & = &30\\\Leftrightarrow & \color{red}{-3}x & = &30\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{30}{-3} \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{+15}& = & 1 \color{red}{ +4x } \\\Leftrightarrow & -11x \color{red}{+15}\color{blue}{-15-4x } & = & 1 \color{red}{ +4x }\color{blue}{-15-4x } \\\Leftrightarrow & -11x \color{blue}{-4x } & = & 1 \color{blue}{-15} \\\Leftrightarrow &-15x & = &-14\\\Leftrightarrow & \color{red}{-15}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-14}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{14}{15} } & & \\ & V = \left\{ \frac{14}{15} \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{+9}& = & -7 \color{red}{ -14x } \\\Leftrightarrow & 3x \color{red}{+9}\color{blue}{-9+14x } & = & -7 \color{red}{ -14x }\color{blue}{-9+14x } \\\Leftrightarrow & 3x \color{blue}{+14x } & = & -7 \color{blue}{-9} \\\Leftrightarrow &17x & = &-16\\\Leftrightarrow & \color{red}{17}x & = &-16\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-16}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{17} } & & \\ & V = \left\{ \frac{-16}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{-3}& = & 4 \color{red}{ -14x } \\\Leftrightarrow & 3x \color{red}{-3}\color{blue}{+3+14x } & = & 4 \color{red}{ -14x }\color{blue}{+3+14x } \\\Leftrightarrow & 3x \color{blue}{+14x } & = & 4 \color{blue}{+3} \\\Leftrightarrow &17x & = &7\\\Leftrightarrow & \color{red}{17}x & = &7\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{7}{17} \\\Leftrightarrow & \color{green}{ x = \frac{7}{17} } & & \\ & V = \left\{ \frac{7}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{-2}& = & 3 \color{red}{ +4x } \\\Leftrightarrow & -x \color{red}{-2}\color{blue}{+2-4x } & = & 3 \color{red}{ +4x }\color{blue}{+2-4x } \\\Leftrightarrow & -x \color{blue}{-4x } & = & 3 \color{blue}{+2} \\\Leftrightarrow &-5x & = &5\\\Leftrightarrow & \color{red}{-5}x & = &5\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{5}{-5} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)