Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -2x \color{red}{+10}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+10}\color{blue}{-10-x } & = & -15 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -15 \color{blue}{-10} \\\Leftrightarrow &-3x & = &-25\\\Leftrightarrow & \color{red}{-3}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-25}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{25}{3} } & & \\ & V = \left\{ \frac{25}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{-9}& = & -3 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{-9}\color{blue}{+9-5x } & = & -3 \color{red}{ +5x }\color{blue}{+9-5x } \\\Leftrightarrow & -2x \color{blue}{-5x } & = & -3 \color{blue}{+9} \\\Leftrightarrow &-7x & = &6\\\Leftrightarrow & \color{red}{-7}x & = &6\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{6}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{-13}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{-13}\color{blue}{+13-x } & = & -1 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & -1 \color{blue}{+13} \\\Leftrightarrow &12x & = &12\\\Leftrightarrow & \color{red}{12}x & = &12\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{12}{12} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{-15}& = & -8 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{-15}\color{blue}{+15+6x } & = & -8 \color{red}{ -6x }\color{blue}{+15+6x } \\\Leftrightarrow & 7x \color{blue}{+6x } & = & -8 \color{blue}{+15} \\\Leftrightarrow &13x & = &7\\\Leftrightarrow & \color{red}{13}x & = &7\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{7}{13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{+3}& = & -8 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+3}\color{blue}{-3+7x } & = & -8 \color{red}{ -7x }\color{blue}{-3+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -8 \color{blue}{-3} \\\Leftrightarrow &15x & = &-11\\\Leftrightarrow & \color{red}{15}x & = &-11\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-11}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{15} } & & \\ & V = \left\{ \frac{-11}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{-1}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-1}\color{blue}{+1-x } & = & -10 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -10 \color{blue}{+1} \\\Leftrightarrow &-5x & = &-9\\\Leftrightarrow & \color{red}{-5}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-9}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{+1}& = & 10 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{+1}\color{blue}{-1+4x } & = & 10 \color{red}{ -4x }\color{blue}{-1+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & 10 \color{blue}{-1} \\\Leftrightarrow &9x & = &9\\\Leftrightarrow & \color{red}{9}x & = &9\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{9}{9} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{-10}& = & 2 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{-10}\color{blue}{+10+9x } & = & 2 \color{red}{ -9x }\color{blue}{+10+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & 2 \color{blue}{+10} \\\Leftrightarrow &19x & = &12\\\Leftrightarrow & \color{red}{19}x & = &12\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{12}{19} \\\Leftrightarrow & \color{green}{ x = \frac{12}{19} } & & \\ & V = \left\{ \frac{12}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{-11}& = & -7 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{-11}\color{blue}{+11-5x } & = & -7 \color{red}{ +5x }\color{blue}{+11-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -7 \color{blue}{+11} \\\Leftrightarrow &7x & = &4\\\Leftrightarrow & \color{red}{7}x & = &4\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{4}{7} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{+1}& = & -11 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{+1}\color{blue}{-1-8x } & = & -11 \color{red}{ +8x }\color{blue}{-1-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & -11 \color{blue}{-1} \\\Leftrightarrow &-15x & = &-12\\\Leftrightarrow & \color{red}{-15}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-12}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{+1}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+1}\color{blue}{-1-x } & = & 12 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 12 \color{blue}{-1} \\\Leftrightarrow &-13x & = &11\\\Leftrightarrow & \color{red}{-13}x & = &11\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{11}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{13} } & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{-1}& = & 3 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{-1}\color{blue}{+1-11x } & = & 3 \color{red}{ +11x }\color{blue}{+1-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & 3 \color{blue}{+1} \\\Leftrightarrow &4x & = &4\\\Leftrightarrow & \color{red}{4}x & = &4\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{4}{4} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)