Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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