Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{+3}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -x \color{red}{+3}\color{blue}{-3-x } & = & 5 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -x \color{blue}{-x } & = & 5 \color{blue}{-3} \\\Leftrightarrow &-2x & = &2\\\Leftrightarrow & \color{red}{-2}x & = &2\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{2}{-2} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{+9}& = & -11 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{+9}\color{blue}{-9-11x } & = & -11 \color{red}{ +11x }\color{blue}{-9-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & -11 \color{blue}{-9} \\\Leftrightarrow &-16x & = &-20\\\Leftrightarrow & \color{red}{-16}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-20}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{+12}& = & 15 \color{red}{ +3x } \\\Leftrightarrow & 7x \color{red}{+12}\color{blue}{-12-3x } & = & 15 \color{red}{ +3x }\color{blue}{-12-3x } \\\Leftrightarrow & 7x \color{blue}{-3x } & = & 15 \color{blue}{-12} \\\Leftrightarrow &4x & = &3\\\Leftrightarrow & \color{red}{4}x & = &3\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{3}{4} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{-1}& = & 1 \color{red}{ +7x } \\\Leftrightarrow & 4x \color{red}{-1}\color{blue}{+1-7x } & = & 1 \color{red}{ +7x }\color{blue}{+1-7x } \\\Leftrightarrow & 4x \color{blue}{-7x } & = & 1 \color{blue}{+1} \\\Leftrightarrow &-3x & = &2\\\Leftrightarrow & \color{red}{-3}x & = &2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{+5}& = & 15 \color{red}{ +12x } \\\Leftrightarrow & x \color{red}{+5}\color{blue}{-5-12x } & = & 15 \color{red}{ +12x }\color{blue}{-5-12x } \\\Leftrightarrow & x \color{blue}{-12x } & = & 15 \color{blue}{-5} \\\Leftrightarrow &-11x & = &10\\\Leftrightarrow & \color{red}{-11}x & = &10\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{10}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{11} } & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{-1}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-1}\color{blue}{+1-x } & = & 11 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 11 \color{blue}{+1} \\\Leftrightarrow &-12x & = &12\\\Leftrightarrow & \color{red}{-12}x & = &12\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{12}{-12} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{+7}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+7}\color{blue}{-7-x } & = & 11 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 11 \color{blue}{-7} \\\Leftrightarrow &-15x & = &4\\\Leftrightarrow & \color{red}{-15}x & = &4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{15} } & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{-3}& = & -9 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{-3}\color{blue}{+3+13x } & = & -9 \color{red}{ -13x }\color{blue}{+3+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & -9 \color{blue}{+3} \\\Leftrightarrow &24x & = &-6\\\Leftrightarrow & \color{red}{24}x & = &-6\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-6}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{-5}& = & -11 \color{red}{ +13x } \\\Leftrightarrow & -2x \color{red}{-5}\color{blue}{+5-13x } & = & -11 \color{red}{ +13x }\color{blue}{+5-13x } \\\Leftrightarrow & -2x \color{blue}{-13x } & = & -11 \color{blue}{+5} \\\Leftrightarrow &-15x & = &-6\\\Leftrightarrow & \color{red}{-15}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-6}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{-12}& = & 2 \color{red}{ +13x } \\\Leftrightarrow & 7x \color{red}{-12}\color{blue}{+12-13x } & = & 2 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & 7x \color{blue}{-13x } & = & 2 \color{blue}{+12} \\\Leftrightarrow &-6x & = &14\\\Leftrightarrow & \color{red}{-6}x & = &14\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{14}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{-3}& = & -3 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-3}\color{blue}{+3+13x } & = & -3 \color{red}{ -13x }\color{blue}{+3+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & -3 \color{blue}{+3} \\\Leftrightarrow &23x & = &0\\\Leftrightarrow & \color{red}{23}x & = &0\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{0}{23} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{+2}& = & 10 \color{red}{ +3x } \\\Leftrightarrow & -14x \color{red}{+2}\color{blue}{-2-3x } & = & 10 \color{red}{ +3x }\color{blue}{-2-3x } \\\Leftrightarrow & -14x \color{blue}{-3x } & = & 10 \color{blue}{-2} \\\Leftrightarrow &-17x & = &8\\\Leftrightarrow & \color{red}{-17}x & = &8\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{8}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{17} } & & \\ & V = \left\{ \frac{-8}{17} \right\} & \\\end{align}\)