Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{+13}& = & -10 \color{red}{ +4x } \\\Leftrightarrow & x \color{red}{+13}\color{blue}{-13-4x } & = & -10 \color{red}{ +4x }\color{blue}{-13-4x } \\\Leftrightarrow & x \color{blue}{-4x } & = & -10 \color{blue}{-13} \\\Leftrightarrow &-3x & = &-23\\\Leftrightarrow & \color{red}{-3}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-23}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{23}{3} } & & \\ & V = \left\{ \frac{23}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{+1}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+1}\color{blue}{-1-x } & = & -6 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -6 \color{blue}{-1} \\\Leftrightarrow &-5x & = &-7\\\Leftrightarrow & \color{red}{-5}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{+15}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+15}\color{blue}{-15-x } & = & -2 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -2 \color{blue}{-15} \\\Leftrightarrow &-11x & = &-17\\\Leftrightarrow & \color{red}{-11}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-17}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{17}{11} } & & \\ & V = \left\{ \frac{17}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{+5}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+5}\color{blue}{-5-x } & = & -12 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -12 \color{blue}{-5} \\\Leftrightarrow &-14x & = &-17\\\Leftrightarrow & \color{red}{-14}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-17}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{17}{14} } & & \\ & V = \left\{ \frac{17}{14} \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{-8}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-8}\color{blue}{+8-x } & = & -3 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -3 \color{blue}{+8} \\\Leftrightarrow &-15x & = &5\\\Leftrightarrow & \color{red}{-15}x & = &5\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{5}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{+4}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+4}\color{blue}{-4-x } & = & -7 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -7 \color{blue}{-4} \\\Leftrightarrow &-3x & = &-11\\\Leftrightarrow & \color{red}{-3}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-11}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{11}{3} } & & \\ & V = \left\{ \frac{11}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{-4}& = & 7 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-4}\color{blue}{+4+7x } & = & 7 \color{red}{ -7x }\color{blue}{+4+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 7 \color{blue}{+4} \\\Leftrightarrow &15x & = &11\\\Leftrightarrow & \color{red}{15}x & = &11\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{11}{15} \\\Leftrightarrow & \color{green}{ x = \frac{11}{15} } & & \\ & V = \left\{ \frac{11}{15} \right\} & \\\end{align}\)
8. \(\begin{align} & -3x \color{red}{-9}& = & 4 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{-9}\color{blue}{+9-7x } & = & 4 \color{red}{ +7x }\color{blue}{+9-7x } \\\Leftrightarrow & -3x \color{blue}{-7x } & = & 4 \color{blue}{+9} \\\Leftrightarrow &-10x & = &13\\\Leftrightarrow & \color{red}{-10}x & = &13\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{13}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{10} } & & \\ & V = \left\{ \frac{-13}{10} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{+12}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{+12}\color{blue}{-12-x } & = & 12 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & 12 \color{blue}{-12} \\\Leftrightarrow &12x & = &0\\\Leftrightarrow & \color{red}{12}x & = &0\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{0}{12} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & x \color{red}{-8}& = & -4 \color{red}{ -8x } \\\Leftrightarrow & x \color{red}{-8}\color{blue}{+8+8x } & = & -4 \color{red}{ -8x }\color{blue}{+8+8x } \\\Leftrightarrow & x \color{blue}{+8x } & = & -4 \color{blue}{+8} \\\Leftrightarrow &9x & = &4\\\Leftrightarrow & \color{red}{9}x & = &4\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{4}{9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{9} } & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{+3}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+3}\color{blue}{-3-x } & = & -13 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -13 \color{blue}{-3} \\\Leftrightarrow &-13x & = &-16\\\Leftrightarrow & \color{red}{-13}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-16}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{16}{13} } & & \\ & V = \left\{ \frac{16}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{+15}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+15}\color{blue}{-15-x } & = & 1 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 1 \color{blue}{-15} \\\Leftrightarrow &-15x & = &-14\\\Leftrightarrow & \color{red}{-15}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-14}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{14}{15} } & & \\ & V = \left\{ \frac{14}{15} \right\} & \\\end{align}\)