Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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