Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{3}{11})& = & -8x+\frac{7}{11} \\\Leftrightarrow & 15x-\frac{15}{11}& = & -8x+\frac{7}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{165}{ \color{blue}{11} }x- \frac{15}{ \color{blue}{11} })& = & (\frac{-88}{ \color{blue}{11} }x+ \frac{7}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 165x \color{red}{-15} & = & \color{red}{-88x} +7 \\\Leftrightarrow & 165x \color{red}{-15} \color{blue}{+15} \color{blue}{+88x} & = & \color{red}{-88x} +7 \color{blue}{+88x} \color{blue}{+15} \\\Leftrightarrow & 165x+88x& = & 7+15 \\\Leftrightarrow & \color{red}{253} x& = & 22 \\\Leftrightarrow & x = \frac{22}{253} & & \\\Leftrightarrow & x = \frac{2}{23} & & \\ & V = \left\{ \frac{2}{23} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{4}{7})& = & 5x+\frac{10}{9} \\\Leftrightarrow & 12x-\frac{16}{7}& = & 5x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{756}{ \color{blue}{63} }x- \frac{144}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 756x \color{red}{-144} & = & \color{red}{315x} +70 \\\Leftrightarrow & 756x \color{red}{-144} \color{blue}{+144} \color{blue}{-315x} & = & \color{red}{315x} +70 \color{blue}{-315x} \color{blue}{+144} \\\Leftrightarrow & 756x-315x& = & 70+144 \\\Leftrightarrow & \color{red}{441} x& = & 214 \\\Leftrightarrow & x = \frac{214}{441} & & \\ & V = \left\{ \frac{214}{441} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{5}{2})& = & -8x+\frac{2}{11} \\\Leftrightarrow & 25x+\frac{25}{2}& = & -8x+\frac{2}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{550}{ \color{blue}{22} }x+ \frac{275}{ \color{blue}{22} })& = & (\frac{-176}{ \color{blue}{22} }x+ \frac{4}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 550x \color{red}{+275} & = & \color{red}{-176x} +4 \\\Leftrightarrow & 550x \color{red}{+275} \color{blue}{-275} \color{blue}{+176x} & = & \color{red}{-176x} +4 \color{blue}{+176x} \color{blue}{-275} \\\Leftrightarrow & 550x+176x& = & 4-275 \\\Leftrightarrow & \color{red}{726} x& = & -271 \\\Leftrightarrow & x = \frac{-271}{726} & & \\ & V = \left\{ \frac{-271}{726} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{4}{11})& = & 9x+\frac{4}{11} \\\Leftrightarrow & 16x+\frac{16}{11}& = & 9x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{176}{ \color{blue}{11} }x+ \frac{16}{ \color{blue}{11} })& = & (\frac{99}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 176x \color{red}{+16} & = & \color{red}{99x} +4 \\\Leftrightarrow & 176x \color{red}{+16} \color{blue}{-16} \color{blue}{-99x} & = & \color{red}{99x} +4 \color{blue}{-99x} \color{blue}{-16} \\\Leftrightarrow & 176x-99x& = & 4-16 \\\Leftrightarrow & \color{red}{77} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{77} & & \\ & V = \left\{ \frac{-12}{77} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{2}{7})& = & -7x+\frac{9}{5} \\\Leftrightarrow & -20x+\frac{8}{7}& = & -7x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-700}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -700x \color{red}{+40} & = & \color{red}{-245x} +63 \\\Leftrightarrow & -700x \color{red}{+40} \color{blue}{-40} \color{blue}{+245x} & = & \color{red}{-245x} +63 \color{blue}{+245x} \color{blue}{-40} \\\Leftrightarrow & -700x+245x& = & 63-40 \\\Leftrightarrow & \color{red}{-455} x& = & 23 \\\Leftrightarrow & x = \frac{23}{-455} & & \\\Leftrightarrow & x = \frac{-23}{455} & & \\ & V = \left\{ \frac{-23}{455} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{5}{11})& = & -9x+\frac{4}{5} \\\Leftrightarrow & -8x-\frac{20}{11}& = & -9x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-440}{ \color{blue}{55} }x- \frac{100}{ \color{blue}{55} })& = & (\frac{-495}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -440x \color{red}{-100} & = & \color{red}{-495x} +44 \\\Leftrightarrow & -440x \color{red}{-100} \color{blue}{+100} \color{blue}{+495x} & = & \color{red}{-495x} +44 \color{blue}{+495x} \color{blue}{+100} \\\Leftrightarrow & -440x+495x& = & 44+100 \\\Leftrightarrow & \color{red}{55} x& = & 144 \\\Leftrightarrow & x = \frac{144}{55} & & \\ & V = \left\{ \frac{144}{55} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{5}{7})& = & -5x+\frac{3}{2} \\\Leftrightarrow & -12x-\frac{30}{7}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-168}{ \color{blue}{14} }x- \frac{60}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -168x \color{red}{-60} & = & \color{red}{-70x} +21 \\\Leftrightarrow & -168x \color{red}{-60} \color{blue}{+60} \color{blue}{+70x} & = & \color{red}{-70x} +21 \color{blue}{+70x} \color{blue}{+60} \\\Leftrightarrow & -168x+70x& = & 21+60 \\\Leftrightarrow & \color{red}{-98} x& = & 81 \\\Leftrightarrow & x = \frac{81}{-98} & & \\\Leftrightarrow & x = \frac{-81}{98} & & \\ & V = \left\{ \frac{-81}{98} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{4}{5})& = & 3x+\frac{4}{3} \\\Leftrightarrow & 8x+\frac{8}{5}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{+24} & = & \color{red}{45x} +20 \\\Leftrightarrow & 120x \color{red}{+24} \color{blue}{-24} \color{blue}{-45x} & = & \color{red}{45x} +20 \color{blue}{-45x} \color{blue}{-24} \\\Leftrightarrow & 120x-45x& = & 20-24 \\\Leftrightarrow & \color{red}{75} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{75} & & \\ & V = \left\{ \frac{-4}{75} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{3}{5})& = & -2x+\frac{6}{11} \\\Leftrightarrow & 15x-\frac{9}{5}& = & -2x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{825}{ \color{blue}{55} }x- \frac{99}{ \color{blue}{55} })& = & (\frac{-110}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 825x \color{red}{-99} & = & \color{red}{-110x} +30 \\\Leftrightarrow & 825x \color{red}{-99} \color{blue}{+99} \color{blue}{+110x} & = & \color{red}{-110x} +30 \color{blue}{+110x} \color{blue}{+99} \\\Leftrightarrow & 825x+110x& = & 30+99 \\\Leftrightarrow & \color{red}{935} x& = & 129 \\\Leftrightarrow & x = \frac{129}{935} & & \\ & V = \left\{ \frac{129}{935} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{3}{4})& = & 4x+\frac{4}{3} \\\Leftrightarrow & 15x+\frac{9}{4}& = & 4x+\frac{4}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{180}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} })& = & (\frac{48}{ \color{blue}{12} }x+ \frac{16}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 180x \color{red}{+27} & = & \color{red}{48x} +16 \\\Leftrightarrow & 180x \color{red}{+27} \color{blue}{-27} \color{blue}{-48x} & = & \color{red}{48x} +16 \color{blue}{-48x} \color{blue}{-27} \\\Leftrightarrow & 180x-48x& = & 16-27 \\\Leftrightarrow & \color{red}{132} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{132} & & \\\Leftrightarrow & x = \frac{-1}{12} & & \\ & V = \left\{ \frac{-1}{12} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{5}{8})& = & 5x+\frac{6}{11} \\\Leftrightarrow & -9x-\frac{15}{8}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-792}{ \color{blue}{88} }x- \frac{165}{ \color{blue}{88} })& = & (\frac{440}{ \color{blue}{88} }x+ \frac{48}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -792x \color{red}{-165} & = & \color{red}{440x} +48 \\\Leftrightarrow & -792x \color{red}{-165} \color{blue}{+165} \color{blue}{-440x} & = & \color{red}{440x} +48 \color{blue}{-440x} \color{blue}{+165} \\\Leftrightarrow & -792x-440x& = & 48+165 \\\Leftrightarrow & \color{red}{-1232} x& = & 213 \\\Leftrightarrow & x = \frac{213}{-1232} & & \\\Leftrightarrow & x = \frac{-213}{1232} & & \\ & V = \left\{ \frac{-213}{1232} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{5}{2})& = & 8x+\frac{5}{2} \\\Leftrightarrow & -15x-\frac{25}{2}& = & 8x+\frac{5}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{-30}{ \color{blue}{2} }x- \frac{25}{ \color{blue}{2} })& = & (\frac{16}{ \color{blue}{2} }x+ \frac{5}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & -30x \color{red}{-25} & = & \color{red}{16x} +5 \\\Leftrightarrow & -30x \color{red}{-25} \color{blue}{+25} \color{blue}{-16x} & = & \color{red}{16x} +5 \color{blue}{-16x} \color{blue}{+25} \\\Leftrightarrow & -30x-16x& = & 5+25 \\\Leftrightarrow & \color{red}{-46} x& = & 30 \\\Leftrightarrow & x = \frac{30}{-46} & & \\\Leftrightarrow & x = \frac{-15}{23} & & \\ & V = \left\{ \frac{-15}{23} \right\} & \\\end{align}\)