Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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