Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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