Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{+10}& = & 4 \color{red}{ +9x } \\\Leftrightarrow & -x \color{red}{+10}\color{blue}{-10-9x } & = & 4 \color{red}{ +9x }\color{blue}{-10-9x } \\\Leftrightarrow & -x \color{blue}{-9x } & = & 4 \color{blue}{-10} \\\Leftrightarrow &-10x & = &-6\\\Leftrightarrow & \color{red}{-10}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-6}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{-4}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{-4}\color{blue}{+4-x } & = & -11 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & -11 \color{blue}{+4} \\\Leftrightarrow &3x & = &-7\\\Leftrightarrow & \color{red}{3}x & = &-7\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-7}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{-9}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-9}\color{blue}{+9-x } & = & -6 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -6 \color{blue}{+9} \\\Leftrightarrow &-5x & = &3\\\Leftrightarrow & \color{red}{-5}x & = &3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{+12}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+12}\color{blue}{-12-x } & = & -8 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -8 \color{blue}{-12} \\\Leftrightarrow &-15x & = &-20\\\Leftrightarrow & \color{red}{-15}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-20}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{-5}& = & -3 \color{red}{ +13x } \\\Leftrightarrow & -x \color{red}{-5}\color{blue}{+5-13x } & = & -3 \color{red}{ +13x }\color{blue}{+5-13x } \\\Leftrightarrow & -x \color{blue}{-13x } & = & -3 \color{blue}{+5} \\\Leftrightarrow &-14x & = &2\\\Leftrightarrow & \color{red}{-14}x & = &2\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{2}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{-10}& = & -12 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-10}\color{blue}{+10-13x } & = & -12 \color{red}{ +13x }\color{blue}{+10-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -12 \color{blue}{+10} \\\Leftrightarrow &-28x & = &-2\\\Leftrightarrow & \color{red}{-28}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-2}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{1}{14} } & & \\ & V = \left\{ \frac{1}{14} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{-4}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-4}\color{blue}{+4-x } & = & 3 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 3 \color{blue}{+4} \\\Leftrightarrow &-7x & = &7\\\Leftrightarrow & \color{red}{-7}x & = &7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{7}{-7} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{+2}& = & -7 \color{red}{ +11x } \\\Leftrightarrow & 14x \color{red}{+2}\color{blue}{-2-11x } & = & -7 \color{red}{ +11x }\color{blue}{-2-11x } \\\Leftrightarrow & 14x \color{blue}{-11x } & = & -7 \color{blue}{-2} \\\Leftrightarrow &3x & = &-9\\\Leftrightarrow & \color{red}{3}x & = &-9\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-9}{3} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{-13}& = & -8 \color{red}{ +10x } \\\Leftrightarrow & 7x \color{red}{-13}\color{blue}{+13-10x } & = & -8 \color{red}{ +10x }\color{blue}{+13-10x } \\\Leftrightarrow & 7x \color{blue}{-10x } & = & -8 \color{blue}{+13} \\\Leftrightarrow &-3x & = &5\\\Leftrightarrow & \color{red}{-3}x & = &5\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{5}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{+7}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+7}\color{blue}{-7-x } & = & 7 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 7 \color{blue}{-7} \\\Leftrightarrow &-9x & = &0\\\Leftrightarrow & \color{red}{-9}x & = &0\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{0}{-9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{+10}& = & -5 \color{red}{ +6x } \\\Leftrightarrow & -11x \color{red}{+10}\color{blue}{-10-6x } & = & -5 \color{red}{ +6x }\color{blue}{-10-6x } \\\Leftrightarrow & -11x \color{blue}{-6x } & = & -5 \color{blue}{-10} \\\Leftrightarrow &-17x & = &-15\\\Leftrightarrow & \color{red}{-17}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-15}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{15}{17} } & & \\ & V = \left\{ \frac{15}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{+10}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+10}\color{blue}{-10-x } & = & 3 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 3 \color{blue}{-10} \\\Leftrightarrow &-10x & = &-7\\\Leftrightarrow & \color{red}{-10}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-7}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{7}{10} } & & \\ & V = \left\{ \frac{7}{10} \right\} & \\\end{align}\)