Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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