Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{+15}& = & -8 \color{red}{ +13x } \\\Leftrightarrow & 6x \color{red}{+15}\color{blue}{-15-13x } & = & -8 \color{red}{ +13x }\color{blue}{-15-13x } \\\Leftrightarrow & 6x \color{blue}{-13x } & = & -8 \color{blue}{-15} \\\Leftrightarrow &-7x & = &-23\\\Leftrightarrow & \color{red}{-7}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-23}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{23}{7} } & & \\ & V = \left\{ \frac{23}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{-15}& = & -7 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{-15}\color{blue}{+15+11x } & = & -7 \color{red}{ -11x }\color{blue}{+15+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & -7 \color{blue}{+15} \\\Leftrightarrow &26x & = &8\\\Leftrightarrow & \color{red}{26}x & = &8\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{8}{26} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{-5}& = & -7 \color{red}{ +4x } \\\Leftrightarrow & x \color{red}{-5}\color{blue}{+5-4x } & = & -7 \color{red}{ +4x }\color{blue}{+5-4x } \\\Leftrightarrow & x \color{blue}{-4x } & = & -7 \color{blue}{+5} \\\Leftrightarrow &-3x & = &-2\\\Leftrightarrow & \color{red}{-3}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{+9}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+9}\color{blue}{-9-x } & = & 5 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 5 \color{blue}{-9} \\\Leftrightarrow &-8x & = &-4\\\Leftrightarrow & \color{red}{-8}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-4}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & -10x \color{red}{+2}& = & 15 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+2}\color{blue}{-2-7x } & = & 15 \color{red}{ +7x }\color{blue}{-2-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 15 \color{blue}{-2} \\\Leftrightarrow &-17x & = &13\\\Leftrightarrow & \color{red}{-17}x & = &13\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{13}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{17} } & & \\ & V = \left\{ \frac{-13}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{-7}& = & -13 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{-7}\color{blue}{+7-8x } & = & -13 \color{red}{ +8x }\color{blue}{+7-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & -13 \color{blue}{+7} \\\Leftrightarrow &-23x & = &-6\\\Leftrightarrow & \color{red}{-23}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-6}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{6}{23} } & & \\ & V = \left\{ \frac{6}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{+7}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+7}\color{blue}{-7-x } & = & -1 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -1 \color{blue}{-7} \\\Leftrightarrow &-15x & = &-8\\\Leftrightarrow & \color{red}{-15}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-8}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{8}{15} } & & \\ & V = \left\{ \frac{8}{15} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{-9}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-9}\color{blue}{+9-x } & = & -15 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -15 \color{blue}{+9} \\\Leftrightarrow &-15x & = &-6\\\Leftrightarrow & \color{red}{-15}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-6}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{+9}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+9}\color{blue}{-9-x } & = & -2 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -2 \color{blue}{-9} \\\Leftrightarrow &-7x & = &-11\\\Leftrightarrow & \color{red}{-7}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-11}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{11}{7} } & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{-2}& = & 12 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{-2}\color{blue}{+2+10x } & = & 12 \color{red}{ -10x }\color{blue}{+2+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & 12 \color{blue}{+2} \\\Leftrightarrow &21x & = &14\\\Leftrightarrow & \color{red}{21}x & = &14\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{14}{21} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{-10}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-10}\color{blue}{+10-x } & = & 12 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 12 \color{blue}{+10} \\\Leftrightarrow &-3x & = &22\\\Leftrightarrow & \color{red}{-3}x & = &22\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{22}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{3} } & & \\ & V = \left\{ \frac{-22}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{+5}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+5}\color{blue}{-5-x } & = & -15 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -15 \color{blue}{-5} \\\Leftrightarrow &-7x & = &-20\\\Leftrightarrow & \color{red}{-7}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-20}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{20}{7} } & & \\ & V = \left\{ \frac{20}{7} \right\} & \\\end{align}\)