Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{5}{4})& = & -7x+\frac{5}{7} \\\Leftrightarrow & 15x+\frac{15}{4}& = & -7x+\frac{5}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{420}{ \color{blue}{28} }x+ \frac{105}{ \color{blue}{28} })& = & (\frac{-196}{ \color{blue}{28} }x+ \frac{20}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 420x \color{red}{+105} & = & \color{red}{-196x} +20 \\\Leftrightarrow & 420x \color{red}{+105} \color{blue}{-105} \color{blue}{+196x} & = & \color{red}{-196x} +20 \color{blue}{+196x} \color{blue}{-105} \\\Leftrightarrow & 420x+196x& = & 20-105 \\\Leftrightarrow & \color{red}{616} x& = & -85 \\\Leftrightarrow & x = \frac{-85}{616} & & \\ & V = \left\{ \frac{-85}{616} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{4}{3})& = & -5x+\frac{7}{3} \\\Leftrightarrow & 6x+\frac{8}{3}& = & -5x+\frac{7}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{18}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} })& = & (\frac{-15}{ \color{blue}{3} }x+ \frac{7}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 18x \color{red}{+8} & = & \color{red}{-15x} +7 \\\Leftrightarrow & 18x \color{red}{+8} \color{blue}{-8} \color{blue}{+15x} & = & \color{red}{-15x} +7 \color{blue}{+15x} \color{blue}{-8} \\\Leftrightarrow & 18x+15x& = & 7-8 \\\Leftrightarrow & \color{red}{33} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{33} & & \\ & V = \left\{ \frac{-1}{33} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{5}{4})& = & 5x+\frac{5}{4} \\\Leftrightarrow & 12x-\frac{15}{4}& = & 5x+\frac{5}{4} \\ & & & \text{kgv van noemers 4 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{48}{ \color{blue}{4} }x- \frac{15}{ \color{blue}{4} })& = & (\frac{20}{ \color{blue}{4} }x+ \frac{5}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 48x \color{red}{-15} & = & \color{red}{20x} +5 \\\Leftrightarrow & 48x \color{red}{-15} \color{blue}{+15} \color{blue}{-20x} & = & \color{red}{20x} +5 \color{blue}{-20x} \color{blue}{+15} \\\Leftrightarrow & 48x-20x& = & 5+15 \\\Leftrightarrow & \color{red}{28} x& = & 20 \\\Leftrightarrow & x = \frac{20}{28} & & \\\Leftrightarrow & x = \frac{5}{7} & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{5}{9})& = & 2x+\frac{9}{10} \\\Leftrightarrow & 25x+\frac{25}{9}& = & 2x+\frac{9}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{2250}{ \color{blue}{90} }x+ \frac{250}{ \color{blue}{90} })& = & (\frac{180}{ \color{blue}{90} }x+ \frac{81}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 2250x \color{red}{+250} & = & \color{red}{180x} +81 \\\Leftrightarrow & 2250x \color{red}{+250} \color{blue}{-250} \color{blue}{-180x} & = & \color{red}{180x} +81 \color{blue}{-180x} \color{blue}{-250} \\\Leftrightarrow & 2250x-180x& = & 81-250 \\\Leftrightarrow & \color{red}{2070} x& = & -169 \\\Leftrightarrow & x = \frac{-169}{2070} & & \\ & V = \left\{ \frac{-169}{2070} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{3}{5})& = & 2x+\frac{8}{7} \\\Leftrightarrow & 9x-\frac{9}{5}& = & 2x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{315}{ \color{blue}{35} }x- \frac{63}{ \color{blue}{35} })& = & (\frac{70}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 315x \color{red}{-63} & = & \color{red}{70x} +40 \\\Leftrightarrow & 315x \color{red}{-63} \color{blue}{+63} \color{blue}{-70x} & = & \color{red}{70x} +40 \color{blue}{-70x} \color{blue}{+63} \\\Leftrightarrow & 315x-70x& = & 40+63 \\\Leftrightarrow & \color{red}{245} x& = & 103 \\\Leftrightarrow & x = \frac{103}{245} & & \\ & V = \left\{ \frac{103}{245} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{2}{5})& = & -5x+\frac{10}{3} \\\Leftrightarrow & 18x+\frac{12}{5}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{270}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 270x \color{red}{+36} & = & \color{red}{-75x} +50 \\\Leftrightarrow & 270x \color{red}{+36} \color{blue}{-36} \color{blue}{+75x} & = & \color{red}{-75x} +50 \color{blue}{+75x} \color{blue}{-36} \\\Leftrightarrow & 270x+75x& = & 50-36 \\\Leftrightarrow & \color{red}{345} x& = & 14 \\\Leftrightarrow & x = \frac{14}{345} & & \\ & V = \left\{ \frac{14}{345} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{3}{5})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -30x-\frac{18}{5}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-450}{ \color{blue}{15} }x- \frac{54}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -450x \color{red}{-54} & = & \color{red}{105x} +20 \\\Leftrightarrow & -450x \color{red}{-54} \color{blue}{+54} \color{blue}{-105x} & = & \color{red}{105x} +20 \color{blue}{-105x} \color{blue}{+54} \\\Leftrightarrow & -450x-105x& = & 20+54 \\\Leftrightarrow & \color{red}{-555} x& = & 74 \\\Leftrightarrow & x = \frac{74}{-555} & & \\\Leftrightarrow & x = \frac{-2}{15} & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{4}{7})& = & 5x+\frac{6}{11} \\\Leftrightarrow & -9x+\frac{12}{7}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-693}{ \color{blue}{77} }x+ \frac{132}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -693x \color{red}{+132} & = & \color{red}{385x} +42 \\\Leftrightarrow & -693x \color{red}{+132} \color{blue}{-132} \color{blue}{-385x} & = & \color{red}{385x} +42 \color{blue}{-385x} \color{blue}{-132} \\\Leftrightarrow & -693x-385x& = & 42-132 \\\Leftrightarrow & \color{red}{-1078} x& = & -90 \\\Leftrightarrow & x = \frac{-90}{-1078} & & \\\Leftrightarrow & x = \frac{45}{539} & & \\ & V = \left\{ \frac{45}{539} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{5}{4})& = & 7x+\frac{5}{9} \\\Leftrightarrow & -20x-\frac{25}{4}& = & 7x+\frac{5}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-720}{ \color{blue}{36} }x- \frac{225}{ \color{blue}{36} })& = & (\frac{252}{ \color{blue}{36} }x+ \frac{20}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -720x \color{red}{-225} & = & \color{red}{252x} +20 \\\Leftrightarrow & -720x \color{red}{-225} \color{blue}{+225} \color{blue}{-252x} & = & \color{red}{252x} +20 \color{blue}{-252x} \color{blue}{+225} \\\Leftrightarrow & -720x-252x& = & 20+225 \\\Leftrightarrow & \color{red}{-972} x& = & 245 \\\Leftrightarrow & x = \frac{245}{-972} & & \\\Leftrightarrow & x = \frac{-245}{972} & & \\ & V = \left\{ \frac{-245}{972} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{3}{7})& = & 3x+\frac{10}{7} \\\Leftrightarrow & -20x+\frac{15}{7}& = & 3x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-140}{ \color{blue}{7} }x+ \frac{15}{ \color{blue}{7} })& = & (\frac{21}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -140x \color{red}{+15} & = & \color{red}{21x} +10 \\\Leftrightarrow & -140x \color{red}{+15} \color{blue}{-15} \color{blue}{-21x} & = & \color{red}{21x} +10 \color{blue}{-21x} \color{blue}{-15} \\\Leftrightarrow & -140x-21x& = & 10-15 \\\Leftrightarrow & \color{red}{-161} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-161} & & \\\Leftrightarrow & x = \frac{5}{161} & & \\ & V = \left\{ \frac{5}{161} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{4}{7})& = & 7x+\frac{9}{2} \\\Leftrightarrow & 4x+\frac{8}{7}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{56}{ \color{blue}{14} }x+ \frac{16}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 56x \color{red}{+16} & = & \color{red}{98x} +63 \\\Leftrightarrow & 56x \color{red}{+16} \color{blue}{-16} \color{blue}{-98x} & = & \color{red}{98x} +63 \color{blue}{-98x} \color{blue}{-16} \\\Leftrightarrow & 56x-98x& = & 63-16 \\\Leftrightarrow & \color{red}{-42} x& = & 47 \\\Leftrightarrow & x = \frac{47}{-42} & & \\\Leftrightarrow & x = \frac{-47}{42} & & \\ & V = \left\{ \frac{-47}{42} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{5}{7})& = & 5x+\frac{3}{8} \\\Leftrightarrow & -12x-\frac{20}{7}& = & 5x+\frac{3}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-672}{ \color{blue}{56} }x- \frac{160}{ \color{blue}{56} })& = & (\frac{280}{ \color{blue}{56} }x+ \frac{21}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -672x \color{red}{-160} & = & \color{red}{280x} +21 \\\Leftrightarrow & -672x \color{red}{-160} \color{blue}{+160} \color{blue}{-280x} & = & \color{red}{280x} +21 \color{blue}{-280x} \color{blue}{+160} \\\Leftrightarrow & -672x-280x& = & 21+160 \\\Leftrightarrow & \color{red}{-952} x& = & 181 \\\Leftrightarrow & x = \frac{181}{-952} & & \\\Leftrightarrow & x = \frac{-181}{952} & & \\ & V = \left\{ \frac{-181}{952} \right\} & \\\end{align}\)