Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 5x \color{red}{+10}& = & 5 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{+10}\color{blue}{-10+4x } & = & 5 \color{red}{ -4x }\color{blue}{-10+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & 5 \color{blue}{-10} \\\Leftrightarrow &9x & = &-5\\\Leftrightarrow & \color{red}{9}x & = &-5\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-5}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{9} } & & \\ & V = \left\{ \frac{-5}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{+15}& = & 13 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+15}\color{blue}{-15+3x } & = & 13 \color{red}{ -3x }\color{blue}{-15+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 13 \color{blue}{-15} \\\Leftrightarrow &13x & = &-2\\\Leftrightarrow & \color{red}{13}x & = &-2\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-2}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{13} } & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{+7}& = & -2 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+7}\color{blue}{-7+11x } & = & -2 \color{red}{ -11x }\color{blue}{-7+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -2 \color{blue}{-7} \\\Leftrightarrow &23x & = &-9\\\Leftrightarrow & \color{red}{23}x & = &-9\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-9}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{23} } & & \\ & V = \left\{ \frac{-9}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{+2}& = & -12 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{+2}\color{blue}{-2-5x } & = & -12 \color{red}{ +5x }\color{blue}{-2-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & -12 \color{blue}{-2} \\\Leftrightarrow &x & = &-14\\\Leftrightarrow & \color{red}{}x & = &-14\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -14 \\\Leftrightarrow & \color{green}{ x = -14 } & & \\ & V = \left\{ -14 \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{+1}& = & -15 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{+1}\color{blue}{-1+3x } & = & -15 \color{red}{ -3x }\color{blue}{-1+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & -15 \color{blue}{-1} \\\Leftrightarrow &10x & = &-16\\\Leftrightarrow & \color{red}{10}x & = &-16\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-16}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{+7}& = & 11 \color{red}{ +8x } \\\Leftrightarrow & -5x \color{red}{+7}\color{blue}{-7-8x } & = & 11 \color{red}{ +8x }\color{blue}{-7-8x } \\\Leftrightarrow & -5x \color{blue}{-8x } & = & 11 \color{blue}{-7} \\\Leftrightarrow &-13x & = &4\\\Leftrightarrow & \color{red}{-13}x & = &4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{+7}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+7}\color{blue}{-7-x } & = & 14 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 14 \color{blue}{-7} \\\Leftrightarrow &-10x & = &7\\\Leftrightarrow & \color{red}{-10}x & = &7\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{7}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{10} } & & \\ & V = \left\{ \frac{-7}{10} \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{-4}& = & -13 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{-4}\color{blue}{+4+9x } & = & -13 \color{red}{ -9x }\color{blue}{+4+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & -13 \color{blue}{+4} \\\Leftrightarrow &14x & = &-9\\\Leftrightarrow & \color{red}{14}x & = &-9\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-9}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{14} } & & \\ & V = \left\{ \frac{-9}{14} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{+5}& = & 10 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{+5}\color{blue}{-5+11x } & = & 10 \color{red}{ -11x }\color{blue}{-5+11x } \\\Leftrightarrow & 9x \color{blue}{+11x } & = & 10 \color{blue}{-5} \\\Leftrightarrow &20x & = &5\\\Leftrightarrow & \color{red}{20}x & = &5\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{5}{20} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{-9}& = & 12 \color{red}{ +10x } \\\Leftrightarrow & 9x \color{red}{-9}\color{blue}{+9-10x } & = & 12 \color{red}{ +10x }\color{blue}{+9-10x } \\\Leftrightarrow & 9x \color{blue}{-10x } & = & 12 \color{blue}{+9} \\\Leftrightarrow &-x & = &21\\\Leftrightarrow & \color{red}{-}x & = &21\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{21}{-1} \\\Leftrightarrow & \color{green}{ x = -21 } & & \\ & V = \left\{ -21 \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{-5}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-5}\color{blue}{+5-x } & = & -14 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -14 \color{blue}{+5} \\\Leftrightarrow &-3x & = &-9\\\Leftrightarrow & \color{red}{-3}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-9}{-3} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{+11}& = & -6 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{+11}\color{blue}{-11-3x } & = & -6 \color{red}{ +3x }\color{blue}{-11-3x } \\\Leftrightarrow & -5x \color{blue}{-3x } & = & -6 \color{blue}{-11} \\\Leftrightarrow &-8x & = &-17\\\Leftrightarrow & \color{red}{-8}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-17}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{17}{8} } & & \\ & V = \left\{ \frac{17}{8} \right\} & \\\end{align}\)