Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{+15}& = & -9 \color{red}{ -8x } \\\Leftrightarrow & x \color{red}{+15}\color{blue}{-15+8x } & = & -9 \color{red}{ -8x }\color{blue}{-15+8x } \\\Leftrightarrow & x \color{blue}{+8x } & = & -9 \color{blue}{-15} \\\Leftrightarrow &9x & = &-24\\\Leftrightarrow & \color{red}{9}x & = &-24\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-24}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{-9}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-9}\color{blue}{+9-x } & = & -1 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -1 \color{blue}{+9} \\\Leftrightarrow &-5x & = &8\\\Leftrightarrow & \color{red}{-5}x & = &8\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{8}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{+10}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+10}\color{blue}{-10-x } & = & -15 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -15 \color{blue}{-10} \\\Leftrightarrow &-15x & = &-25\\\Leftrightarrow & \color{red}{-15}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-25}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{+12}& = & 7 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{+12}\color{blue}{-12-11x } & = & 7 \color{red}{ +11x }\color{blue}{-12-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & 7 \color{blue}{-12} \\\Leftrightarrow &x & = &-5\\\Leftrightarrow & \color{red}{}x & = &-5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -5 \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{+10}& = & 6 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{+10}\color{blue}{-10+13x } & = & 6 \color{red}{ -13x }\color{blue}{-10+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & 6 \color{blue}{-10} \\\Leftrightarrow &23x & = &-4\\\Leftrightarrow & \color{red}{23}x & = &-4\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-4}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{23} } & & \\ & V = \left\{ \frac{-4}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{-1}& = & -11 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{-1}\color{blue}{+1-3x } & = & -11 \color{red}{ +3x }\color{blue}{+1-3x } \\\Leftrightarrow & -2x \color{blue}{-3x } & = & -11 \color{blue}{+1} \\\Leftrightarrow &-5x & = &-10\\\Leftrightarrow & \color{red}{-5}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-10}{-5} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{+9}& = & -11 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{+9}\color{blue}{-9+14x } & = & -11 \color{red}{ -14x }\color{blue}{-9+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & -11 \color{blue}{-9} \\\Leftrightarrow &19x & = &-20\\\Leftrightarrow & \color{red}{19}x & = &-20\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-20}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{19} } & & \\ & V = \left\{ \frac{-20}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{-3}& = & 10 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{-3}\color{blue}{+3-5x } & = & 10 \color{red}{ +5x }\color{blue}{+3-5x } \\\Leftrightarrow & -2x \color{blue}{-5x } & = & 10 \color{blue}{+3} \\\Leftrightarrow &-7x & = &13\\\Leftrightarrow & \color{red}{-7}x & = &13\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{13}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{7} } & & \\ & V = \left\{ \frac{-13}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{-3}& = & 6 \color{red}{ -4x } \\\Leftrightarrow & -x \color{red}{-3}\color{blue}{+3+4x } & = & 6 \color{red}{ -4x }\color{blue}{+3+4x } \\\Leftrightarrow & -x \color{blue}{+4x } & = & 6 \color{blue}{+3} \\\Leftrightarrow &3x & = &9\\\Leftrightarrow & \color{red}{3}x & = &9\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{9}{3} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{-6}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-6}\color{blue}{+6-x } & = & 3 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 3 \color{blue}{+6} \\\Leftrightarrow &-15x & = &9\\\Leftrightarrow & \color{red}{-15}x & = &9\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{9}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{-9}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-9}\color{blue}{+9-x } & = & 7 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 7 \color{blue}{+9} \\\Leftrightarrow &-7x & = &16\\\Leftrightarrow & \color{red}{-7}x & = &16\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{16}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{7} } & & \\ & V = \left\{ \frac{-16}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{-11}& = & 7 \color{red}{ +15x } \\\Leftrightarrow & x \color{red}{-11}\color{blue}{+11-15x } & = & 7 \color{red}{ +15x }\color{blue}{+11-15x } \\\Leftrightarrow & x \color{blue}{-15x } & = & 7 \color{blue}{+11} \\\Leftrightarrow &-14x & = &18\\\Leftrightarrow & \color{red}{-14}x & = &18\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{18}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)