Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -14x \color{red}{+6}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+6}\color{blue}{-6-x } & = & 13 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 13 \color{blue}{-6} \\\Leftrightarrow &-15x & = &7\\\Leftrightarrow & \color{red}{-15}x & = &7\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{7}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{15} } & & \\ & V = \left\{ \frac{-7}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{-9}& = & -7 \color{red}{ +11x } \\\Leftrightarrow & -2x \color{red}{-9}\color{blue}{+9-11x } & = & -7 \color{red}{ +11x }\color{blue}{+9-11x } \\\Leftrightarrow & -2x \color{blue}{-11x } & = & -7 \color{blue}{+9} \\\Leftrightarrow &-13x & = &2\\\Leftrightarrow & \color{red}{-13}x & = &2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{13} } & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{-15}& = & 8 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-15}\color{blue}{+15+11x } & = & 8 \color{red}{ -11x }\color{blue}{+15+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 8 \color{blue}{+15} \\\Leftrightarrow &23x & = &23\\\Leftrightarrow & \color{red}{23}x & = &23\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{23}{23} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{+1}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+1}\color{blue}{-1-x } & = & 5 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 5 \color{blue}{-1} \\\Leftrightarrow &-12x & = &4\\\Leftrightarrow & \color{red}{-12}x & = &4\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{4}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{+3}& = & -4 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{+3}\color{blue}{-3+11x } & = & -4 \color{red}{ -11x }\color{blue}{-3+11x } \\\Leftrightarrow & 14x \color{blue}{+11x } & = & -4 \color{blue}{-3} \\\Leftrightarrow &25x & = &-7\\\Leftrightarrow & \color{red}{25}x & = &-7\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{-7}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{25} } & & \\ & V = \left\{ \frac{-7}{25} \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{-6}& = & -12 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-6}\color{blue}{+6+3x } & = & -12 \color{red}{ -3x }\color{blue}{+6+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & -12 \color{blue}{+6} \\\Leftrightarrow &13x & = &-6\\\Leftrightarrow & \color{red}{13}x & = &-6\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-6}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{13} } & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{+15}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+15}\color{blue}{-15-x } & = & -13 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -13 \color{blue}{-15} \\\Leftrightarrow &-16x & = &-28\\\Leftrightarrow & \color{red}{-16}x & = &-28\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-28}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{7}{4} } & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{-6}& = & 6 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{-6}\color{blue}{+6+8x } & = & 6 \color{red}{ -8x }\color{blue}{+6+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & 6 \color{blue}{+6} \\\Leftrightarrow &17x & = &12\\\Leftrightarrow & \color{red}{17}x & = &12\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{12}{17} \\\Leftrightarrow & \color{green}{ x = \frac{12}{17} } & & \\ & V = \left\{ \frac{12}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{-2}& = & -5 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{-2}\color{blue}{+2-13x } & = & -5 \color{red}{ +13x }\color{blue}{+2-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & -5 \color{blue}{+2} \\\Leftrightarrow &-3x & = &-3\\\Leftrightarrow & \color{red}{-3}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-3}{-3} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{-5}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-5}\color{blue}{+5-x } & = & -10 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -10 \color{blue}{+5} \\\Leftrightarrow &-8x & = &-5\\\Leftrightarrow & \color{red}{-8}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-5}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{-5}& = & 1 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{-5}\color{blue}{+5+11x } & = & 1 \color{red}{ -11x }\color{blue}{+5+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & 1 \color{blue}{+5} \\\Leftrightarrow &15x & = &6\\\Leftrightarrow & \color{red}{15}x & = &6\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{6}{15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{-1}& = & 13 \color{red}{ -x } \\\Leftrightarrow & x \color{red}{-1}\color{blue}{+1+x } & = & 13 \color{red}{ -x }\color{blue}{+1+x } \\\Leftrightarrow & x \color{blue}{+x } & = & 13 \color{blue}{+1} \\\Leftrightarrow &2x & = &14\\\Leftrightarrow & \color{red}{2}x & = &14\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{14}{2} \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)