Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{+8}& = & -1 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{+8}\color{blue}{-8+11x } & = & -1 \color{red}{ -11x }\color{blue}{-8+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & -1 \color{blue}{-8} \\\Leftrightarrow &15x & = &-9\\\Leftrightarrow & \color{red}{15}x & = &-9\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-9}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{-15}& = & -10 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-15}\color{blue}{+15+7x } & = & -10 \color{red}{ -7x }\color{blue}{+15+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -10 \color{blue}{+15} \\\Leftrightarrow &15x & = &5\\\Leftrightarrow & \color{red}{15}x & = &5\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{5}{15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{+3}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+3}\color{blue}{-3-x } & = & -12 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -12 \color{blue}{-3} \\\Leftrightarrow &-12x & = &-15\\\Leftrightarrow & \color{red}{-12}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-15}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{+13}& = & 3 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+13}\color{blue}{-13-7x } & = & 3 \color{red}{ +7x }\color{blue}{-13-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 3 \color{blue}{-13} \\\Leftrightarrow &-17x & = &-10\\\Leftrightarrow & \color{red}{-17}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-10}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{10}{17} } & & \\ & V = \left\{ \frac{10}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{+6}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+6}\color{blue}{-6-x } & = & -1 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -1 \color{blue}{-6} \\\Leftrightarrow &-15x & = &-7\\\Leftrightarrow & \color{red}{-15}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-7}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{7}{15} } & & \\ & V = \left\{ \frac{7}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & -6x \color{red}{-10}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-10}\color{blue}{+10-x } & = & 2 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 2 \color{blue}{+10} \\\Leftrightarrow &-7x & = &12\\\Leftrightarrow & \color{red}{-7}x & = &12\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{12}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{7} } & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{+13}& = & 2 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{+13}\color{blue}{-13-x } & = & 2 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & 2 \color{blue}{-13} \\\Leftrightarrow &3x & = &-11\\\Leftrightarrow & \color{red}{3}x & = &-11\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-11}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{3} } & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{-5}& = & -10 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{-5}\color{blue}{+5-6x } & = & -10 \color{red}{ +6x }\color{blue}{+5-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & -10 \color{blue}{+5} \\\Leftrightarrow &-11x & = &-5\\\Leftrightarrow & \color{red}{-11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{-10}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-10}\color{blue}{+10-x } & = & 4 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 4 \color{blue}{+10} \\\Leftrightarrow &-16x & = &14\\\Leftrightarrow & \color{red}{-16}x & = &14\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{14}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{8} } & & \\ & V = \left\{ \frac{-7}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{+8}& = & -10 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+8}\color{blue}{-8+11x } & = & -10 \color{red}{ -11x }\color{blue}{-8+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -10 \color{blue}{-8} \\\Leftrightarrow &23x & = &-18\\\Leftrightarrow & \color{red}{23}x & = &-18\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-18}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{23} } & & \\ & V = \left\{ \frac{-18}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{-9}& = & 14 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{-9}\color{blue}{+9-x } & = & 14 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & 14 \color{blue}{+9} \\\Leftrightarrow &3x & = &23\\\Leftrightarrow & \color{red}{3}x & = &23\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{23}{3} \\\Leftrightarrow & \color{green}{ x = \frac{23}{3} } & & \\ & V = \left\{ \frac{23}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{+6}& = & -3 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+6}\color{blue}{-6-7x } & = & -3 \color{red}{ +7x }\color{blue}{-6-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -3 \color{blue}{-6} \\\Leftrightarrow &-17x & = &-9\\\Leftrightarrow & \color{red}{-17}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-9}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{9}{17} } & & \\ & V = \left\{ \frac{9}{17} \right\} & \\\end{align}\)