Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{-12}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-12}\color{blue}{+12-x } & = & -14 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -14 \color{blue}{+12} \\\Leftrightarrow &-7x & = &-2\\\Leftrightarrow & \color{red}{-7}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{+9}& = & 5 \color{red}{ +4x } \\\Leftrightarrow & 3x \color{red}{+9}\color{blue}{-9-4x } & = & 5 \color{red}{ +4x }\color{blue}{-9-4x } \\\Leftrightarrow & 3x \color{blue}{-4x } & = & 5 \color{blue}{-9} \\\Leftrightarrow &-x & = &-4\\\Leftrightarrow & \color{red}{-}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-4}{-1} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{-6}& = & -1 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{-6}\color{blue}{+6+15x } & = & -1 \color{red}{ -15x }\color{blue}{+6+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & -1 \color{blue}{+6} \\\Leftrightarrow &23x & = &5\\\Leftrightarrow & \color{red}{23}x & = &5\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{5}{23} \\\Leftrightarrow & \color{green}{ x = \frac{5}{23} } & & \\ & V = \left\{ \frac{5}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{-9}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-9}\color{blue}{+9-x } & = & 3 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 3 \color{blue}{+9} \\\Leftrightarrow &-7x & = &12\\\Leftrightarrow & \color{red}{-7}x & = &12\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{12}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{7} } & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{-3}& = & -4 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-3}\color{blue}{+3+11x } & = & -4 \color{red}{ -11x }\color{blue}{+3+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -4 \color{blue}{+3} \\\Leftrightarrow &23x & = &-1\\\Leftrightarrow & \color{red}{23}x & = &-1\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-1}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{23} } & & \\ & V = \left\{ \frac{-1}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{-6}& = & 1 \color{red}{ +2x } \\\Leftrightarrow & 5x \color{red}{-6}\color{blue}{+6-2x } & = & 1 \color{red}{ +2x }\color{blue}{+6-2x } \\\Leftrightarrow & 5x \color{blue}{-2x } & = & 1 \color{blue}{+6} \\\Leftrightarrow &3x & = &7\\\Leftrightarrow & \color{red}{3}x & = &7\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{7}{3} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{+9}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+9}\color{blue}{-9-x } & = & 3 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 3 \color{blue}{-9} \\\Leftrightarrow &-16x & = &-6\\\Leftrightarrow & \color{red}{-16}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-6}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{-13}& = & -11 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-13}\color{blue}{+13-13x } & = & -11 \color{red}{ +13x }\color{blue}{+13-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -11 \color{blue}{+13} \\\Leftrightarrow &-25x & = &2\\\Leftrightarrow & \color{red}{-25}x & = &2\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{2}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{25} } & & \\ & V = \left\{ \frac{-2}{25} \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{-4}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-4}\color{blue}{+4-x } & = & -10 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -10 \color{blue}{+4} \\\Leftrightarrow &-3x & = &-6\\\Leftrightarrow & \color{red}{-3}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-6}{-3} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{+12}& = & 1 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{+12}\color{blue}{-12-5x } & = & 1 \color{red}{ +5x }\color{blue}{-12-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & 1 \color{blue}{-12} \\\Leftrightarrow &-9x & = &-11\\\Leftrightarrow & \color{red}{-9}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-11}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{11}{9} } & & \\ & V = \left\{ \frac{11}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{-7}& = & -5 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{-7}\color{blue}{+7+2x } & = & -5 \color{red}{ -2x }\color{blue}{+7+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & -5 \color{blue}{+7} \\\Leftrightarrow &17x & = &2\\\Leftrightarrow & \color{red}{17}x & = &2\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{2}{17} \\\Leftrightarrow & \color{green}{ x = \frac{2}{17} } & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{-13}& = & -11 \color{red}{ +7x } \\\Leftrightarrow & 9x \color{red}{-13}\color{blue}{+13-7x } & = & -11 \color{red}{ +7x }\color{blue}{+13-7x } \\\Leftrightarrow & 9x \color{blue}{-7x } & = & -11 \color{blue}{+13} \\\Leftrightarrow &2x & = &2\\\Leftrightarrow & \color{red}{2}x & = &2\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{2}{2} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)