Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{3}{11})& = & 7x+\frac{3}{2} \\\Leftrightarrow & -30x+\frac{18}{11}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-660}{ \color{blue}{22} }x+ \frac{36}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -660x \color{red}{+36} & = & \color{red}{154x} +33 \\\Leftrightarrow & -660x \color{red}{+36} \color{blue}{-36} \color{blue}{-154x} & = & \color{red}{154x} +33 \color{blue}{-154x} \color{blue}{-36} \\\Leftrightarrow & -660x-154x& = & 33-36 \\\Leftrightarrow & \color{red}{-814} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-814} & & \\\Leftrightarrow & x = \frac{3}{814} & & \\ & V = \left\{ \frac{3}{814} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{2}{3})& = & -5x+\frac{10}{7} \\\Leftrightarrow & -28x-\frac{14}{3}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-588}{ \color{blue}{21} }x- \frac{98}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -588x \color{red}{-98} & = & \color{red}{-105x} +30 \\\Leftrightarrow & -588x \color{red}{-98} \color{blue}{+98} \color{blue}{+105x} & = & \color{red}{-105x} +30 \color{blue}{+105x} \color{blue}{+98} \\\Leftrightarrow & -588x+105x& = & 30+98 \\\Leftrightarrow & \color{red}{-483} x& = & 128 \\\Leftrightarrow & x = \frac{128}{-483} & & \\\Leftrightarrow & x = \frac{-128}{483} & & \\ & V = \left\{ \frac{-128}{483} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{5}{4})& = & -5x+\frac{3}{10} \\\Leftrightarrow & -12x-\frac{15}{4}& = & -5x+\frac{3}{10} \\ & & & \text{kgv van noemers 4 en 10 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-240}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{-100}{ \color{blue}{20} }x+ \frac{6}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -240x \color{red}{-75} & = & \color{red}{-100x} +6 \\\Leftrightarrow & -240x \color{red}{-75} \color{blue}{+75} \color{blue}{+100x} & = & \color{red}{-100x} +6 \color{blue}{+100x} \color{blue}{+75} \\\Leftrightarrow & -240x+100x& = & 6+75 \\\Leftrightarrow & \color{red}{-140} x& = & 81 \\\Leftrightarrow & x = \frac{81}{-140} & & \\\Leftrightarrow & x = \frac{-81}{140} & & \\ & V = \left\{ \frac{-81}{140} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{4}{11})& = & -7x+\frac{4}{5} \\\Leftrightarrow & 30x-\frac{24}{11}& = & -7x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1650}{ \color{blue}{55} }x- \frac{120}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1650x \color{red}{-120} & = & \color{red}{-385x} +44 \\\Leftrightarrow & 1650x \color{red}{-120} \color{blue}{+120} \color{blue}{+385x} & = & \color{red}{-385x} +44 \color{blue}{+385x} \color{blue}{+120} \\\Leftrightarrow & 1650x+385x& = & 44+120 \\\Leftrightarrow & \color{red}{2035} x& = & 164 \\\Leftrightarrow & x = \frac{164}{2035} & & \\ & V = \left\{ \frac{164}{2035} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{5}{11})& = & -3x+\frac{3}{10} \\\Leftrightarrow & 16x-\frac{20}{11}& = & -3x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{1760}{ \color{blue}{110} }x- \frac{200}{ \color{blue}{110} })& = & (\frac{-330}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 1760x \color{red}{-200} & = & \color{red}{-330x} +33 \\\Leftrightarrow & 1760x \color{red}{-200} \color{blue}{+200} \color{blue}{+330x} & = & \color{red}{-330x} +33 \color{blue}{+330x} \color{blue}{+200} \\\Leftrightarrow & 1760x+330x& = & 33+200 \\\Leftrightarrow & \color{red}{2090} x& = & 233 \\\Leftrightarrow & x = \frac{233}{2090} & & \\ & V = \left\{ \frac{233}{2090} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{5}{3})& = & 9x+\frac{7}{2} \\\Leftrightarrow & 8x+\frac{20}{3}& = & 9x+\frac{7}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{48}{ \color{blue}{6} }x+ \frac{40}{ \color{blue}{6} })& = & (\frac{54}{ \color{blue}{6} }x+ \frac{21}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 48x \color{red}{+40} & = & \color{red}{54x} +21 \\\Leftrightarrow & 48x \color{red}{+40} \color{blue}{-40} \color{blue}{-54x} & = & \color{red}{54x} +21 \color{blue}{-54x} \color{blue}{-40} \\\Leftrightarrow & 48x-54x& = & 21-40 \\\Leftrightarrow & \color{red}{-6} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{-6} & & \\\Leftrightarrow & x = \frac{19}{6} & & \\ & V = \left\{ \frac{19}{6} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{4}{11})& = & -7x+\frac{5}{11} \\\Leftrightarrow & 12x-\frac{16}{11}& = & -7x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{132}{ \color{blue}{11} }x- \frac{16}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 132x \color{red}{-16} & = & \color{red}{-77x} +5 \\\Leftrightarrow & 132x \color{red}{-16} \color{blue}{+16} \color{blue}{+77x} & = & \color{red}{-77x} +5 \color{blue}{+77x} \color{blue}{+16} \\\Leftrightarrow & 132x+77x& = & 5+16 \\\Leftrightarrow & \color{red}{209} x& = & 21 \\\Leftrightarrow & x = \frac{21}{209} & & \\ & V = \left\{ \frac{21}{209} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{2}{5})& = & 5x+\frac{4}{5} \\\Leftrightarrow & 24x+\frac{12}{5}& = & 5x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{120}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 120x \color{red}{+12} & = & \color{red}{25x} +4 \\\Leftrightarrow & 120x \color{red}{+12} \color{blue}{-12} \color{blue}{-25x} & = & \color{red}{25x} +4 \color{blue}{-25x} \color{blue}{-12} \\\Leftrightarrow & 120x-25x& = & 4-12 \\\Leftrightarrow & \color{red}{95} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{95} & & \\ & V = \left\{ \frac{-8}{95} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{3}{11})& = & -5x+\frac{9}{2} \\\Leftrightarrow & 16x-\frac{12}{11}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{352}{ \color{blue}{22} }x- \frac{24}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 352x \color{red}{-24} & = & \color{red}{-110x} +99 \\\Leftrightarrow & 352x \color{red}{-24} \color{blue}{+24} \color{blue}{+110x} & = & \color{red}{-110x} +99 \color{blue}{+110x} \color{blue}{+24} \\\Leftrightarrow & 352x+110x& = & 99+24 \\\Leftrightarrow & \color{red}{462} x& = & 123 \\\Leftrightarrow & x = \frac{123}{462} & & \\\Leftrightarrow & x = \frac{41}{154} & & \\ & V = \left\{ \frac{41}{154} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{4}{3})& = & -5x+\frac{2}{7} \\\Leftrightarrow & -4x+\frac{8}{3}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-84}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -84x \color{red}{+56} & = & \color{red}{-105x} +6 \\\Leftrightarrow & -84x \color{red}{+56} \color{blue}{-56} \color{blue}{+105x} & = & \color{red}{-105x} +6 \color{blue}{+105x} \color{blue}{-56} \\\Leftrightarrow & -84x+105x& = & 6-56 \\\Leftrightarrow & \color{red}{21} x& = & -50 \\\Leftrightarrow & x = \frac{-50}{21} & & \\ & V = \left\{ \frac{-50}{21} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{5}{7})& = & -7x+\frac{9}{2} \\\Leftrightarrow & -24x+\frac{30}{7}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-336}{ \color{blue}{14} }x+ \frac{60}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -336x \color{red}{+60} & = & \color{red}{-98x} +63 \\\Leftrightarrow & -336x \color{red}{+60} \color{blue}{-60} \color{blue}{+98x} & = & \color{red}{-98x} +63 \color{blue}{+98x} \color{blue}{-60} \\\Leftrightarrow & -336x+98x& = & 63-60 \\\Leftrightarrow & \color{red}{-238} x& = & 3 \\\Leftrightarrow & x = \frac{3}{-238} & & \\\Leftrightarrow & x = \frac{-3}{238} & & \\ & V = \left\{ \frac{-3}{238} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{4}{5})& = & -2x+\frac{6}{5} \\\Leftrightarrow & 21x-\frac{28}{5}& = & -2x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{105}{ \color{blue}{5} }x- \frac{28}{ \color{blue}{5} })& = & (\frac{-10}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 105x \color{red}{-28} & = & \color{red}{-10x} +6 \\\Leftrightarrow & 105x \color{red}{-28} \color{blue}{+28} \color{blue}{+10x} & = & \color{red}{-10x} +6 \color{blue}{+10x} \color{blue}{+28} \\\Leftrightarrow & 105x+10x& = & 6+28 \\\Leftrightarrow & \color{red}{115} x& = & 34 \\\Leftrightarrow & x = \frac{34}{115} & & \\ & V = \left\{ \frac{34}{115} \right\} & \\\end{align}\)