Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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