Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{+5}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+5}\color{blue}{-5-x } & = & -10 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -10 \color{blue}{-5} \\\Leftrightarrow &-4x & = &-15\\\Leftrightarrow & \color{red}{-4}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-15}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{15}{4} } & & \\ & V = \left\{ \frac{15}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{+10}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+10}\color{blue}{-10-x } & = & -6 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -6 \color{blue}{-10} \\\Leftrightarrow &-12x & = &-16\\\Leftrightarrow & \color{red}{-12}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-16}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{+15}& = & -9 \color{red}{ +14x } \\\Leftrightarrow & 13x \color{red}{+15}\color{blue}{-15-14x } & = & -9 \color{red}{ +14x }\color{blue}{-15-14x } \\\Leftrightarrow & 13x \color{blue}{-14x } & = & -9 \color{blue}{-15} \\\Leftrightarrow &-x & = &-24\\\Leftrightarrow & \color{red}{-}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-24}{-1} \\\Leftrightarrow & \color{green}{ x = 24 } & & \\ & V = \left\{ 24 \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{+4}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 15x \color{red}{+4}\color{blue}{-4-x } & = & -6 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 15x \color{blue}{-x } & = & -6 \color{blue}{-4} \\\Leftrightarrow &14x & = &-10\\\Leftrightarrow & \color{red}{14}x & = &-10\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-10}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{+10}& = & 12 \color{red}{ +8x } \\\Leftrightarrow & 11x \color{red}{+10}\color{blue}{-10-8x } & = & 12 \color{red}{ +8x }\color{blue}{-10-8x } \\\Leftrightarrow & 11x \color{blue}{-8x } & = & 12 \color{blue}{-10} \\\Leftrightarrow &3x & = &2\\\Leftrightarrow & \color{red}{3}x & = &2\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{2}{3} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{-8}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-8}\color{blue}{+8-x } & = & 15 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 15 \color{blue}{+8} \\\Leftrightarrow &-3x & = &23\\\Leftrightarrow & \color{red}{-3}x & = &23\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{23}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{3} } & & \\ & V = \left\{ \frac{-23}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{-9}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-9}\color{blue}{+9-x } & = & -5 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -5 \color{blue}{+9} \\\Leftrightarrow &-7x & = &4\\\Leftrightarrow & \color{red}{-7}x & = &4\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{4}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{-4}& = & -12 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{-4}\color{blue}{+4-9x } & = & -12 \color{red}{ +9x }\color{blue}{+4-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & -12 \color{blue}{+4} \\\Leftrightarrow &-13x & = &-8\\\Leftrightarrow & \color{red}{-13}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-8}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{8}{13} } & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{+13}& = & -1 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+13}\color{blue}{-13+13x } & = & -1 \color{red}{ -13x }\color{blue}{-13+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -1 \color{blue}{-13} \\\Leftrightarrow &27x & = &-14\\\Leftrightarrow & \color{red}{27}x & = &-14\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-14}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{27} } & & \\ & V = \left\{ \frac{-14}{27} \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{+10}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+10}\color{blue}{-10-x } & = & 3 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 3 \color{blue}{-10} \\\Leftrightarrow &-5x & = &-7\\\Leftrightarrow & \color{red}{-5}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{-13}& = & 5 \color{red}{ +3x } \\\Leftrightarrow & 14x \color{red}{-13}\color{blue}{+13-3x } & = & 5 \color{red}{ +3x }\color{blue}{+13-3x } \\\Leftrightarrow & 14x \color{blue}{-3x } & = & 5 \color{blue}{+13} \\\Leftrightarrow &11x & = &18\\\Leftrightarrow & \color{red}{11}x & = &18\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{18}{11} \\\Leftrightarrow & \color{green}{ x = \frac{18}{11} } & & \\ & V = \left\{ \frac{18}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{-4}& = & -2 \color{red}{ +3x } \\\Leftrightarrow & 14x \color{red}{-4}\color{blue}{+4-3x } & = & -2 \color{red}{ +3x }\color{blue}{+4-3x } \\\Leftrightarrow & 14x \color{blue}{-3x } & = & -2 \color{blue}{+4} \\\Leftrightarrow &11x & = &2\\\Leftrightarrow & \color{red}{11}x & = &2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{2}{11} } & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)