Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{+10}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+10}\color{blue}{-10-x } & = & -5 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -5 \color{blue}{-10} \\\Leftrightarrow &-9x & = &-15\\\Leftrightarrow & \color{red}{-9}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-15}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{+8}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+8}\color{blue}{-8-x } & = & 14 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 14 \color{blue}{-8} \\\Leftrightarrow &-5x & = &6\\\Leftrightarrow & \color{red}{-5}x & = &6\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{6}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{+7}& = & -14 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{+7}\color{blue}{-7+4x } & = & -14 \color{red}{ -4x }\color{blue}{-7+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & -14 \color{blue}{-7} \\\Leftrightarrow &13x & = &-21\\\Leftrightarrow & \color{red}{13}x & = &-21\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-21}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{13} } & & \\ & V = \left\{ \frac{-21}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{+3}& = & -4 \color{red}{ +11x } \\\Leftrightarrow & 14x \color{red}{+3}\color{blue}{-3-11x } & = & -4 \color{red}{ +11x }\color{blue}{-3-11x } \\\Leftrightarrow & 14x \color{blue}{-11x } & = & -4 \color{blue}{-3} \\\Leftrightarrow &3x & = &-7\\\Leftrightarrow & \color{red}{3}x & = &-7\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-7}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{-10}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-10}\color{blue}{+10-x } & = & 15 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 15 \color{blue}{+10} \\\Leftrightarrow &-7x & = &25\\\Leftrightarrow & \color{red}{-7}x & = &25\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{25}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{7} } & & \\ & V = \left\{ \frac{-25}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{+12}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+12}\color{blue}{-12-x } & = & -8 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -8 \color{blue}{-12} \\\Leftrightarrow &-3x & = &-20\\\Leftrightarrow & \color{red}{-3}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-20}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{20}{3} } & & \\ & V = \left\{ \frac{20}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{-7}& = & 10 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{-7}\color{blue}{+7-9x } & = & 10 \color{red}{ +9x }\color{blue}{+7-9x } \\\Leftrightarrow & -11x \color{blue}{-9x } & = & 10 \color{blue}{+7} \\\Leftrightarrow &-20x & = &17\\\Leftrightarrow & \color{red}{-20}x & = &17\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{17}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{20} } & & \\ & V = \left\{ \frac{-17}{20} \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{-6}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-6}\color{blue}{+6-x } & = & -10 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -10 \color{blue}{+6} \\\Leftrightarrow &-6x & = &-4\\\Leftrightarrow & \color{red}{-6}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-4}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{-1}& = & 12 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{-1}\color{blue}{+1+11x } & = & 12 \color{red}{ -11x }\color{blue}{+1+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & 12 \color{blue}{+1} \\\Leftrightarrow &15x & = &13\\\Leftrightarrow & \color{red}{15}x & = &13\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{13}{15} \\\Leftrightarrow & \color{green}{ x = \frac{13}{15} } & & \\ & V = \left\{ \frac{13}{15} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{+5}& = & 15 \color{red}{ +9x } \\\Leftrightarrow & 7x \color{red}{+5}\color{blue}{-5-9x } & = & 15 \color{red}{ +9x }\color{blue}{-5-9x } \\\Leftrightarrow & 7x \color{blue}{-9x } & = & 15 \color{blue}{-5} \\\Leftrightarrow &-2x & = &10\\\Leftrightarrow & \color{red}{-2}x & = &10\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{10}{-2} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
11. \(\begin{align} & 12x \color{red}{+3}& = & 7 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{+3}\color{blue}{-3-5x } & = & 7 \color{red}{ +5x }\color{blue}{-3-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & 7 \color{blue}{-3} \\\Leftrightarrow &7x & = &4\\\Leftrightarrow & \color{red}{7}x & = &4\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{4}{7} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{+2}& = & 2 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+2}\color{blue}{-2-x } & = & 2 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 2 \color{blue}{-2} \\\Leftrightarrow &x & = &0\\\Leftrightarrow & \color{red}{}x & = &0\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 0 \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)