Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{3}{5})& = & 9x+\frac{8}{7} \\\Leftrightarrow & -8x+\frac{12}{5}& = & 9x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{+84} & = & \color{red}{315x} +40 \\\Leftrightarrow & -280x \color{red}{+84} \color{blue}{-84} \color{blue}{-315x} & = & \color{red}{315x} +40 \color{blue}{-315x} \color{blue}{-84} \\\Leftrightarrow & -280x-315x& = & 40-84 \\\Leftrightarrow & \color{red}{-595} x& = & -44 \\\Leftrightarrow & x = \frac{-44}{-595} & & \\\Leftrightarrow & x = \frac{44}{595} & & \\ & V = \left\{ \frac{44}{595} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{2}{9})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -28x+\frac{14}{9}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1764}{ \color{blue}{63} }x+ \frac{98}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1764x \color{red}{+98} & = & \color{red}{441x} +90 \\\Leftrightarrow & -1764x \color{red}{+98} \color{blue}{-98} \color{blue}{-441x} & = & \color{red}{441x} +90 \color{blue}{-441x} \color{blue}{-98} \\\Leftrightarrow & -1764x-441x& = & 90-98 \\\Leftrightarrow & \color{red}{-2205} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-2205} & & \\\Leftrightarrow & x = \frac{8}{2205} & & \\ & V = \left\{ \frac{8}{2205} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{4}{9})& = & -9x+\frac{2}{3} \\\Leftrightarrow & -20x+\frac{16}{9}& = & -9x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-180}{ \color{blue}{9} }x+ \frac{16}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -180x \color{red}{+16} & = & \color{red}{-81x} +6 \\\Leftrightarrow & -180x \color{red}{+16} \color{blue}{-16} \color{blue}{+81x} & = & \color{red}{-81x} +6 \color{blue}{+81x} \color{blue}{-16} \\\Leftrightarrow & -180x+81x& = & 6-16 \\\Leftrightarrow & \color{red}{-99} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-99} & & \\\Leftrightarrow & x = \frac{10}{99} & & \\ & V = \left\{ \frac{10}{99} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{3}{8})& = & 9x+\frac{6}{11} \\\Leftrightarrow & 28x+\frac{21}{8}& = & 9x+\frac{6}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{2464}{ \color{blue}{88} }x+ \frac{231}{ \color{blue}{88} })& = & (\frac{792}{ \color{blue}{88} }x+ \frac{48}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 2464x \color{red}{+231} & = & \color{red}{792x} +48 \\\Leftrightarrow & 2464x \color{red}{+231} \color{blue}{-231} \color{blue}{-792x} & = & \color{red}{792x} +48 \color{blue}{-792x} \color{blue}{-231} \\\Leftrightarrow & 2464x-792x& = & 48-231 \\\Leftrightarrow & \color{red}{1672} x& = & -183 \\\Leftrightarrow & x = \frac{-183}{1672} & & \\ & V = \left\{ \frac{-183}{1672} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{3}{11})& = & -5x+\frac{3}{5} \\\Leftrightarrow & -12x+\frac{12}{11}& = & -5x+\frac{3}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x+ \frac{60}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{33}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{+60} & = & \color{red}{-275x} +33 \\\Leftrightarrow & -660x \color{red}{+60} \color{blue}{-60} \color{blue}{+275x} & = & \color{red}{-275x} +33 \color{blue}{+275x} \color{blue}{-60} \\\Leftrightarrow & -660x+275x& = & 33-60 \\\Leftrightarrow & \color{red}{-385} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{-385} & & \\\Leftrightarrow & x = \frac{27}{385} & & \\ & V = \left\{ \frac{27}{385} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{3}{11})& = & 7x+\frac{4}{5} \\\Leftrightarrow & 15x+\frac{15}{11}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{825}{ \color{blue}{55} }x+ \frac{75}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 825x \color{red}{+75} & = & \color{red}{385x} +44 \\\Leftrightarrow & 825x \color{red}{+75} \color{blue}{-75} \color{blue}{-385x} & = & \color{red}{385x} +44 \color{blue}{-385x} \color{blue}{-75} \\\Leftrightarrow & 825x-385x& = & 44-75 \\\Leftrightarrow & \color{red}{440} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{440} & & \\ & V = \left\{ \frac{-31}{440} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{4}{5})& = & 4x+\frac{10}{9} \\\Leftrightarrow & 21x+\frac{28}{5}& = & 4x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{945}{ \color{blue}{45} }x+ \frac{252}{ \color{blue}{45} })& = & (\frac{180}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 945x \color{red}{+252} & = & \color{red}{180x} +50 \\\Leftrightarrow & 945x \color{red}{+252} \color{blue}{-252} \color{blue}{-180x} & = & \color{red}{180x} +50 \color{blue}{-180x} \color{blue}{-252} \\\Leftrightarrow & 945x-180x& = & 50-252 \\\Leftrightarrow & \color{red}{765} x& = & -202 \\\Leftrightarrow & x = \frac{-202}{765} & & \\ & V = \left\{ \frac{-202}{765} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{3}{7})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -6x+\frac{9}{7}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{+27} & = & \color{red}{-147x} +70 \\\Leftrightarrow & -126x \color{red}{+27} \color{blue}{-27} \color{blue}{+147x} & = & \color{red}{-147x} +70 \color{blue}{+147x} \color{blue}{-27} \\\Leftrightarrow & -126x+147x& = & 70-27 \\\Leftrightarrow & \color{red}{21} x& = & 43 \\\Leftrightarrow & x = \frac{43}{21} & & \\ & V = \left\{ \frac{43}{21} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{3}{5})& = & 3x+\frac{6}{7} \\\Leftrightarrow & 20x+\frac{12}{5}& = & 3x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{700}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 700x \color{red}{+84} & = & \color{red}{105x} +30 \\\Leftrightarrow & 700x \color{red}{+84} \color{blue}{-84} \color{blue}{-105x} & = & \color{red}{105x} +30 \color{blue}{-105x} \color{blue}{-84} \\\Leftrightarrow & 700x-105x& = & 30-84 \\\Leftrightarrow & \color{red}{595} x& = & -54 \\\Leftrightarrow & x = \frac{-54}{595} & & \\ & V = \left\{ \frac{-54}{595} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{4}{11})& = & -4x+\frac{6}{5} \\\Leftrightarrow & -15x+\frac{20}{11}& = & -4x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-825}{ \color{blue}{55} }x+ \frac{100}{ \color{blue}{55} })& = & (\frac{-220}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -825x \color{red}{+100} & = & \color{red}{-220x} +66 \\\Leftrightarrow & -825x \color{red}{+100} \color{blue}{-100} \color{blue}{+220x} & = & \color{red}{-220x} +66 \color{blue}{+220x} \color{blue}{-100} \\\Leftrightarrow & -825x+220x& = & 66-100 \\\Leftrightarrow & \color{red}{-605} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{-605} & & \\\Leftrightarrow & x = \frac{34}{605} & & \\ & V = \left\{ \frac{34}{605} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{5}{11})& = & 9x+\frac{5}{11} \\\Leftrightarrow & 28x+\frac{35}{11}& = & 9x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{308}{ \color{blue}{11} }x+ \frac{35}{ \color{blue}{11} })& = & (\frac{99}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 308x \color{red}{+35} & = & \color{red}{99x} +5 \\\Leftrightarrow & 308x \color{red}{+35} \color{blue}{-35} \color{blue}{-99x} & = & \color{red}{99x} +5 \color{blue}{-99x} \color{blue}{-35} \\\Leftrightarrow & 308x-99x& = & 5-35 \\\Leftrightarrow & \color{red}{209} x& = & -30 \\\Leftrightarrow & x = \frac{-30}{209} & & \\ & V = \left\{ \frac{-30}{209} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{5}{6})& = & -6x+\frac{5}{11} \\\Leftrightarrow & -25x-\frac{25}{6}& = & -6x+\frac{5}{11} \\ & & & \text{kgv van noemers 6 en 11 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-1650}{ \color{blue}{66} }x- \frac{275}{ \color{blue}{66} })& = & (\frac{-396}{ \color{blue}{66} }x+ \frac{30}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -1650x \color{red}{-275} & = & \color{red}{-396x} +30 \\\Leftrightarrow & -1650x \color{red}{-275} \color{blue}{+275} \color{blue}{+396x} & = & \color{red}{-396x} +30 \color{blue}{+396x} \color{blue}{+275} \\\Leftrightarrow & -1650x+396x& = & 30+275 \\\Leftrightarrow & \color{red}{-1254} x& = & 305 \\\Leftrightarrow & x = \frac{305}{-1254} & & \\\Leftrightarrow & x = \frac{-305}{1254} & & \\ & V = \left\{ \frac{-305}{1254} \right\} & \\\end{align}\)