Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{+5}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+5}\color{blue}{-5-x } & = & -14 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -14 \color{blue}{-5} \\\Leftrightarrow &x & = &-19\\\Leftrightarrow & \color{red}{}x & = &-19\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -19 \\\Leftrightarrow & \color{green}{ x = -19 } & & \\ & V = \left\{ -19 \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{-1}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-1}\color{blue}{+1-x } & = & -13 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -13 \color{blue}{+1} \\\Leftrightarrow &-8x & = &-12\\\Leftrightarrow & \color{red}{-8}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-12}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{+15}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+15}\color{blue}{-15-x } & = & 4 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 4 \color{blue}{-15} \\\Leftrightarrow &-15x & = &-11\\\Leftrightarrow & \color{red}{-15}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-11}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{11}{15} } & & \\ & V = \left\{ \frac{11}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{+8}& = & -6 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{+8}\color{blue}{-8+11x } & = & -6 \color{red}{ -11x }\color{blue}{-8+11x } \\\Leftrightarrow & 3x \color{blue}{+11x } & = & -6 \color{blue}{-8} \\\Leftrightarrow &14x & = &-14\\\Leftrightarrow & \color{red}{14}x & = &-14\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-14}{14} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{-7}& = & -2 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{-7}\color{blue}{+7-x } & = & -2 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & -2 \color{blue}{+7} \\\Leftrightarrow &2x & = &5\\\Leftrightarrow & \color{red}{2}x & = &5\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{5}{2} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{+11}& = & -14 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{+11}\color{blue}{-11-7x } & = & -14 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & -14 \color{blue}{-11} \\\Leftrightarrow &-5x & = &-25\\\Leftrightarrow & \color{red}{-5}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-25}{-5} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{+1}& = & -2 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+1}\color{blue}{-1+3x } & = & -2 \color{red}{ -3x }\color{blue}{-1+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & -2 \color{blue}{-1} \\\Leftrightarrow &13x & = &-3\\\Leftrightarrow & \color{red}{13}x & = &-3\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-3}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{-4}& = & -7 \color{red}{ +4x } \\\Leftrightarrow & 9x \color{red}{-4}\color{blue}{+4-4x } & = & -7 \color{red}{ +4x }\color{blue}{+4-4x } \\\Leftrightarrow & 9x \color{blue}{-4x } & = & -7 \color{blue}{+4} \\\Leftrightarrow &5x & = &-3\\\Leftrightarrow & \color{red}{5}x & = &-3\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-3}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{+9}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+9}\color{blue}{-9-x } & = & -15 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -15 \color{blue}{-9} \\\Leftrightarrow &-8x & = &-24\\\Leftrightarrow & \color{red}{-8}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-24}{-8} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{+9}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+9}\color{blue}{-9-x } & = & -3 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -3 \color{blue}{-9} \\\Leftrightarrow &x & = &-12\\\Leftrightarrow & \color{red}{}x & = &-12\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -12 \\\Leftrightarrow & \color{green}{ x = -12 } & & \\ & V = \left\{ -12 \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{+11}& = & -6 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{+11}\color{blue}{-11+8x } & = & -6 \color{red}{ -8x }\color{blue}{-11+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & -6 \color{blue}{-11} \\\Leftrightarrow &11x & = &-17\\\Leftrightarrow & \color{red}{11}x & = &-17\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-17}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{11} } & & \\ & V = \left\{ \frac{-17}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{+15}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{+15}\color{blue}{-15-x } & = & 8 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & 8 \color{blue}{-15} \\\Leftrightarrow &3x & = &-7\\\Leftrightarrow & \color{red}{3}x & = &-7\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-7}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)