Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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