Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -14x \color{red}{-8}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-8}\color{blue}{+8-x } & = & -14 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -14 \color{blue}{+8} \\\Leftrightarrow &-15x & = &-6\\\Leftrightarrow & \color{red}{-15}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-6}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{+12}& = & 14 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+12}\color{blue}{-12-x } & = & 14 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 14 \color{blue}{-12} \\\Leftrightarrow &11x & = &2\\\Leftrightarrow & \color{red}{11}x & = &2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{2}{11} } & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{+8}& = & -7 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{+8}\color{blue}{-8+4x } & = & -7 \color{red}{ -4x }\color{blue}{-8+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & -7 \color{blue}{-8} \\\Leftrightarrow &9x & = &-15\\\Leftrightarrow & \color{red}{9}x & = &-15\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-15}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{-10}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-10}\color{blue}{+10-x } & = & -14 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -14 \color{blue}{+10} \\\Leftrightarrow &-8x & = &-4\\\Leftrightarrow & \color{red}{-8}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-4}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{-7}& = & 5 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-7}\color{blue}{+7+7x } & = & 5 \color{red}{ -7x }\color{blue}{+7+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 5 \color{blue}{+7} \\\Leftrightarrow &15x & = &12\\\Leftrightarrow & \color{red}{15}x & = &12\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{12}{15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{-6}& = & 15 \color{red}{ +9x } \\\Leftrightarrow & 4x \color{red}{-6}\color{blue}{+6-9x } & = & 15 \color{red}{ +9x }\color{blue}{+6-9x } \\\Leftrightarrow & 4x \color{blue}{-9x } & = & 15 \color{blue}{+6} \\\Leftrightarrow &-5x & = &21\\\Leftrightarrow & \color{red}{-5}x & = &21\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{21}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{5} } & & \\ & V = \left\{ \frac{-21}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{+2}& = & 10 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{+2}\color{blue}{-2-9x } & = & 10 \color{red}{ +9x }\color{blue}{-2-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & 10 \color{blue}{-2} \\\Leftrightarrow &-13x & = &8\\\Leftrightarrow & \color{red}{-13}x & = &8\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{8}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{13} } & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{-10}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-10}\color{blue}{+10-x } & = & 3 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 3 \color{blue}{+10} \\\Leftrightarrow &-12x & = &13\\\Leftrightarrow & \color{red}{-12}x & = &13\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{13}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{12} } & & \\ & V = \left\{ \frac{-13}{12} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{-15}& = & -14 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{-15}\color{blue}{+15-13x } & = & -14 \color{red}{ +13x }\color{blue}{+15-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & -14 \color{blue}{+15} \\\Leftrightarrow &-17x & = &1\\\Leftrightarrow & \color{red}{-17}x & = &1\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{1}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{17} } & & \\ & V = \left\{ \frac{-1}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{-4}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-4}\color{blue}{+4-x } & = & 13 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 13 \color{blue}{+4} \\\Leftrightarrow &13x & = &17\\\Leftrightarrow & \color{red}{13}x & = &17\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{17}{13} \\\Leftrightarrow & \color{green}{ x = \frac{17}{13} } & & \\ & V = \left\{ \frac{17}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{+5}& = & 10 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{+5}\color{blue}{-5-10x } & = & 10 \color{red}{ +10x }\color{blue}{-5-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & 10 \color{blue}{-5} \\\Leftrightarrow &-13x & = &5\\\Leftrightarrow & \color{red}{-13}x & = &5\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{5}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{-5}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-5}\color{blue}{+5-x } & = & -6 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -6 \color{blue}{+5} \\\Leftrightarrow &-15x & = &-1\\\Leftrightarrow & \color{red}{-15}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{15} } & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)