Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{-11}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-11}\color{blue}{+11-x } & = & -11 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -11 \color{blue}{+11} \\\Leftrightarrow &7x & = &0\\\Leftrightarrow & \color{red}{7}x & = &0\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{0}{7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{-6}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-6}\color{blue}{+6-x } & = & 11 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 11 \color{blue}{+6} \\\Leftrightarrow &-7x & = &17\\\Leftrightarrow & \color{red}{-7}x & = &17\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{17}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{7} } & & \\ & V = \left\{ \frac{-17}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{+7}& = & -11 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+7}\color{blue}{-7+3x } & = & -11 \color{red}{ -3x }\color{blue}{-7+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & -11 \color{blue}{-7} \\\Leftrightarrow &13x & = &-18\\\Leftrightarrow & \color{red}{13}x & = &-18\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-18}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{13} } & & \\ & V = \left\{ \frac{-18}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{+1}& = & 1 \color{red}{ +11x } \\\Leftrightarrow & 9x \color{red}{+1}\color{blue}{-1-11x } & = & 1 \color{red}{ +11x }\color{blue}{-1-11x } \\\Leftrightarrow & 9x \color{blue}{-11x } & = & 1 \color{blue}{-1} \\\Leftrightarrow &-2x & = &0\\\Leftrightarrow & \color{red}{-2}x & = &0\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{0}{-2} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{-15}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{-15}\color{blue}{+15-x } & = & -11 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & -11 \color{blue}{+15} \\\Leftrightarrow &3x & = &4\\\Leftrightarrow & \color{red}{3}x & = &4\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{4}{3} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{+12}& = & -6 \color{red}{ +7x } \\\Leftrightarrow & 4x \color{red}{+12}\color{blue}{-12-7x } & = & -6 \color{red}{ +7x }\color{blue}{-12-7x } \\\Leftrightarrow & 4x \color{blue}{-7x } & = & -6 \color{blue}{-12} \\\Leftrightarrow &-3x & = &-18\\\Leftrightarrow & \color{red}{-3}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-18}{-3} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{-10}& = & -3 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{-10}\color{blue}{+10+2x } & = & -3 \color{red}{ -2x }\color{blue}{+10+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & -3 \color{blue}{+10} \\\Leftrightarrow &17x & = &7\\\Leftrightarrow & \color{red}{17}x & = &7\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{7}{17} \\\Leftrightarrow & \color{green}{ x = \frac{7}{17} } & & \\ & V = \left\{ \frac{7}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{-9}& = & 12 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{-9}\color{blue}{+9-11x } & = & 12 \color{red}{ +11x }\color{blue}{+9-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & 12 \color{blue}{+9} \\\Leftrightarrow &-5x & = &21\\\Leftrightarrow & \color{red}{-5}x & = &21\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{21}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{5} } & & \\ & V = \left\{ \frac{-21}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{-10}& = & 12 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{-10}\color{blue}{+10-5x } & = & 12 \color{red}{ +5x }\color{blue}{+10-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & 12 \color{blue}{+10} \\\Leftrightarrow &x & = &22\\\Leftrightarrow & \color{red}{}x & = &22\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 22 \\\Leftrightarrow & \color{green}{ x = 22 } & & \\ & V = \left\{ 22 \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{-13}& = & -6 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{-13}\color{blue}{+13-5x } & = & -6 \color{red}{ +5x }\color{blue}{+13-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & -6 \color{blue}{+13} \\\Leftrightarrow &-17x & = &7\\\Leftrightarrow & \color{red}{-17}x & = &7\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{7}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{17} } & & \\ & V = \left\{ \frac{-7}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{+4}& = & -11 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{+4}\color{blue}{-4-14x } & = & -11 \color{red}{ +14x }\color{blue}{-4-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & -11 \color{blue}{-4} \\\Leftrightarrow &-23x & = &-15\\\Leftrightarrow & \color{red}{-23}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-15}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{15}{23} } & & \\ & V = \left\{ \frac{15}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{+3}& = & -3 \color{red}{ +8x } \\\Leftrightarrow & 5x \color{red}{+3}\color{blue}{-3-8x } & = & -3 \color{red}{ +8x }\color{blue}{-3-8x } \\\Leftrightarrow & 5x \color{blue}{-8x } & = & -3 \color{blue}{-3} \\\Leftrightarrow &-3x & = &-6\\\Leftrightarrow & \color{red}{-3}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-6}{-3} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)