Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{-15}& = & -14 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{-15}\color{blue}{+15+11x } & = & -14 \color{red}{ -11x }\color{blue}{+15+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & -14 \color{blue}{+15} \\\Leftrightarrow &15x & = &1\\\Leftrightarrow & \color{red}{15}x & = &1\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{1}{15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{15} } & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{-1}& = & 1 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{-1}\color{blue}{+1-13x } & = & 1 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & 1 \color{blue}{+1} \\\Leftrightarrow &-16x & = &2\\\Leftrightarrow & \color{red}{-16}x & = &2\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{2}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{+4}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+4}\color{blue}{-4-x } & = & 3 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 3 \color{blue}{-4} \\\Leftrightarrow &-5x & = &-1\\\Leftrightarrow & \color{red}{-5}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{-14}& = & 6 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{-14}\color{blue}{+14+8x } & = & 6 \color{red}{ -8x }\color{blue}{+14+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & 6 \color{blue}{+14} \\\Leftrightarrow &11x & = &20\\\Leftrightarrow & \color{red}{11}x & = &20\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{20}{11} \\\Leftrightarrow & \color{green}{ x = \frac{20}{11} } & & \\ & V = \left\{ \frac{20}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{-4}& = & 7 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-4}\color{blue}{+4-9x } & = & 7 \color{red}{ +9x }\color{blue}{+4-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 7 \color{blue}{+4} \\\Leftrightarrow &-17x & = &11\\\Leftrightarrow & \color{red}{-17}x & = &11\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{11}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{17} } & & \\ & V = \left\{ \frac{-11}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{-14}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-14}\color{blue}{+14-x } & = & -14 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -14 \color{blue}{+14} \\\Leftrightarrow &-13x & = &0\\\Leftrightarrow & \color{red}{-13}x & = &0\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{0}{-13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{+2}& = & -13 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{+2}\color{blue}{-2-12x } & = & -13 \color{red}{ +12x }\color{blue}{-2-12x } \\\Leftrightarrow & -11x \color{blue}{-12x } & = & -13 \color{blue}{-2} \\\Leftrightarrow &-23x & = &-15\\\Leftrightarrow & \color{red}{-23}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-15}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{15}{23} } & & \\ & V = \left\{ \frac{15}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{-13}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-13}\color{blue}{+13-x } & = & -14 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -14 \color{blue}{+13} \\\Leftrightarrow &-15x & = &-1\\\Leftrightarrow & \color{red}{-15}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{15} } & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{+6}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+6}\color{blue}{-6-x } & = & 2 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 2 \color{blue}{-6} \\\Leftrightarrow &-16x & = &-4\\\Leftrightarrow & \color{red}{-16}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-4}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{-6}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-6}\color{blue}{+6-x } & = & 3 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 3 \color{blue}{+6} \\\Leftrightarrow &x & = &9\\\Leftrightarrow & \color{red}{}x & = &9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 9 \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{-3}& = & 2 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{-3}\color{blue}{+3-10x } & = & 2 \color{red}{ +10x }\color{blue}{+3-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & 2 \color{blue}{+3} \\\Leftrightarrow &-13x & = &5\\\Leftrightarrow & \color{red}{-13}x & = &5\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{5}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{-12}& = & -5 \color{red}{ +9x } \\\Leftrightarrow & -13x \color{red}{-12}\color{blue}{+12-9x } & = & -5 \color{red}{ +9x }\color{blue}{+12-9x } \\\Leftrightarrow & -13x \color{blue}{-9x } & = & -5 \color{blue}{+12} \\\Leftrightarrow &-22x & = &7\\\Leftrightarrow & \color{red}{-22}x & = &7\\\Leftrightarrow & \frac{\color{red}{-22}x}{ \color{blue}{ -22}} & = & \frac{7}{-22} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{22} } & & \\ & V = \left\{ \frac{-7}{22} \right\} & \\\end{align}\)