Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{+4}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+4}\color{blue}{-4-x } & = & 4 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 4 \color{blue}{-4} \\\Leftrightarrow &-10x & = &0\\\Leftrightarrow & \color{red}{-10}x & = &0\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{0}{-10} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{+11}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+11}\color{blue}{-11-x } & = & 3 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 3 \color{blue}{-11} \\\Leftrightarrow &-8x & = &-8\\\Leftrightarrow & \color{red}{-8}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-8}{-8} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{-11}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 15x \color{red}{-11}\color{blue}{+11-x } & = & 12 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 15x \color{blue}{-x } & = & 12 \color{blue}{+11} \\\Leftrightarrow &14x & = &23\\\Leftrightarrow & \color{red}{14}x & = &23\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{23}{14} \\\Leftrightarrow & \color{green}{ x = \frac{23}{14} } & & \\ & V = \left\{ \frac{23}{14} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{-4}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-4}\color{blue}{+4-x } & = & -14 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -14 \color{blue}{+4} \\\Leftrightarrow &x & = &-10\\\Leftrightarrow & \color{red}{}x & = &-10\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -10 \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{-9}& = & -11 \color{red}{ +4x } \\\Leftrightarrow & 7x \color{red}{-9}\color{blue}{+9-4x } & = & -11 \color{red}{ +4x }\color{blue}{+9-4x } \\\Leftrightarrow & 7x \color{blue}{-4x } & = & -11 \color{blue}{+9} \\\Leftrightarrow &3x & = &-2\\\Leftrightarrow & \color{red}{3}x & = &-2\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-2}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{-8}& = & -4 \color{red}{ +6x } \\\Leftrightarrow & 13x \color{red}{-8}\color{blue}{+8-6x } & = & -4 \color{red}{ +6x }\color{blue}{+8-6x } \\\Leftrightarrow & 13x \color{blue}{-6x } & = & -4 \color{blue}{+8} \\\Leftrightarrow &7x & = &4\\\Leftrightarrow & \color{red}{7}x & = &4\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{4}{7} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{+11}& = & 6 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+11}\color{blue}{-11+13x } & = & 6 \color{red}{ -13x }\color{blue}{-11+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & 6 \color{blue}{-11} \\\Leftrightarrow &24x & = &-5\\\Leftrightarrow & \color{red}{24}x & = &-5\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-5}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{24} } & & \\ & V = \left\{ \frac{-5}{24} \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{-1}& = & 9 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{-1}\color{blue}{+1+14x } & = & 9 \color{red}{ -14x }\color{blue}{+1+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & 9 \color{blue}{+1} \\\Leftrightarrow &19x & = &10\\\Leftrightarrow & \color{red}{19}x & = &10\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{10}{19} \\\Leftrightarrow & \color{green}{ x = \frac{10}{19} } & & \\ & V = \left\{ \frac{10}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & x \color{red}{+2}& = & -7 \color{red}{ -9x } \\\Leftrightarrow & x \color{red}{+2}\color{blue}{-2+9x } & = & -7 \color{red}{ -9x }\color{blue}{-2+9x } \\\Leftrightarrow & x \color{blue}{+9x } & = & -7 \color{blue}{-2} \\\Leftrightarrow &10x & = &-9\\\Leftrightarrow & \color{red}{10}x & = &-9\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-9}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{10} } & & \\ & V = \left\{ \frac{-9}{10} \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{+10}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+10}\color{blue}{-10-x } & = & 3 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 3 \color{blue}{-10} \\\Leftrightarrow &-4x & = &-7\\\Leftrightarrow & \color{red}{-4}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-7}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{4} } & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{-1}& = & -2 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-1}\color{blue}{+1-9x } & = & -2 \color{red}{ +9x }\color{blue}{+1-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -2 \color{blue}{+1} \\\Leftrightarrow &-17x & = &-1\\\Leftrightarrow & \color{red}{-17}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-1}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{1}{17} } & & \\ & V = \left\{ \frac{1}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{-15}& = & 14 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{-15}\color{blue}{+15-5x } & = & 14 \color{red}{ +5x }\color{blue}{+15-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & 14 \color{blue}{+15} \\\Leftrightarrow &-14x & = &29\\\Leftrightarrow & \color{red}{-14}x & = &29\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{29}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{14} } & & \\ & V = \left\{ \frac{-29}{14} \right\} & \\\end{align}\)