Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{-5}& = & -14 \color{red}{ +7x } \\\Leftrightarrow & 6x \color{red}{-5}\color{blue}{+5-7x } & = & -14 \color{red}{ +7x }\color{blue}{+5-7x } \\\Leftrightarrow & 6x \color{blue}{-7x } & = & -14 \color{blue}{+5} \\\Leftrightarrow &-x & = &-9\\\Leftrightarrow & \color{red}{-}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-9}{-1} \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{-8}& = & 9 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{-8}\color{blue}{+8-7x } & = & 9 \color{red}{ +7x }\color{blue}{+8-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & 9 \color{blue}{+8} \\\Leftrightarrow &8x & = &17\\\Leftrightarrow & \color{red}{8}x & = &17\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{17}{8} \\\Leftrightarrow & \color{green}{ x = \frac{17}{8} } & & \\ & V = \left\{ \frac{17}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{-6}& = & -3 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-6}\color{blue}{+6+13x } & = & -3 \color{red}{ -13x }\color{blue}{+6+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -3 \color{blue}{+6} \\\Leftrightarrow &27x & = &3\\\Leftrightarrow & \color{red}{27}x & = &3\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{3}{27} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{+1}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+1}\color{blue}{-1-x } & = & 4 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 4 \color{blue}{-1} \\\Leftrightarrow &-6x & = &3\\\Leftrightarrow & \color{red}{-6}x & = &3\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{3}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{+10}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+10}\color{blue}{-10-x } & = & 7 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 7 \color{blue}{-10} \\\Leftrightarrow &-8x & = &-3\\\Leftrightarrow & \color{red}{-8}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-3}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{+10}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+10}\color{blue}{-10-x } & = & -5 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -5 \color{blue}{-10} \\\Leftrightarrow &-11x & = &-15\\\Leftrightarrow & \color{red}{-11}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-15}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{15}{11} } & & \\ & V = \left\{ \frac{15}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{+9}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+9}\color{blue}{-9-x } & = & -10 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -10 \color{blue}{-9} \\\Leftrightarrow &-9x & = &-19\\\Leftrightarrow & \color{red}{-9}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-19}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{19}{9} } & & \\ & V = \left\{ \frac{19}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{+10}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+10}\color{blue}{-10-x } & = & 14 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 14 \color{blue}{-10} \\\Leftrightarrow &-15x & = &4\\\Leftrightarrow & \color{red}{-15}x & = &4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{15} } & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{+15}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+15}\color{blue}{-15-x } & = & 1 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 1 \color{blue}{-15} \\\Leftrightarrow &5x & = &-14\\\Leftrightarrow & \color{red}{5}x & = &-14\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-14}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{5} } & & \\ & V = \left\{ \frac{-14}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{+12}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+12}\color{blue}{-12-x } & = & 2 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 2 \color{blue}{-12} \\\Leftrightarrow &-12x & = &-10\\\Leftrightarrow & \color{red}{-12}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-10}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{-4}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & 8x \color{red}{-4}\color{blue}{+4-7x } & = & -7 \color{red}{ +7x }\color{blue}{+4-7x } \\\Leftrightarrow & 8x \color{blue}{-7x } & = & -7 \color{blue}{+4} \\\Leftrightarrow &x & = &-3\\\Leftrightarrow & \color{red}{}x & = &-3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -3 \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{+15}& = & -5 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{+15}\color{blue}{-15-11x } & = & -5 \color{red}{ +11x }\color{blue}{-15-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & -5 \color{blue}{-15} \\\Leftrightarrow &-5x & = &-20\\\Leftrightarrow & \color{red}{-5}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-20}{-5} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)