Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{5}{7})& = & 5x+\frac{8}{3} \\\Leftrightarrow & 24x-\frac{30}{7}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{504}{ \color{blue}{21} }x- \frac{90}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 504x \color{red}{-90} & = & \color{red}{105x} +56 \\\Leftrightarrow & 504x \color{red}{-90} \color{blue}{+90} \color{blue}{-105x} & = & \color{red}{105x} +56 \color{blue}{-105x} \color{blue}{+90} \\\Leftrightarrow & 504x-105x& = & 56+90 \\\Leftrightarrow & \color{red}{399} x& = & 146 \\\Leftrightarrow & x = \frac{146}{399} & & \\ & V = \left\{ \frac{146}{399} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{3}{7})& = & 7x+\frac{10}{9} \\\Leftrightarrow & 10x+\frac{6}{7}& = & 7x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{630}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 630x \color{red}{+54} & = & \color{red}{441x} +70 \\\Leftrightarrow & 630x \color{red}{+54} \color{blue}{-54} \color{blue}{-441x} & = & \color{red}{441x} +70 \color{blue}{-441x} \color{blue}{-54} \\\Leftrightarrow & 630x-441x& = & 70-54 \\\Leftrightarrow & \color{red}{189} x& = & 16 \\\Leftrightarrow & x = \frac{16}{189} & & \\ & V = \left\{ \frac{16}{189} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{2}{5})& = & -7x+\frac{8}{11} \\\Leftrightarrow & -30x-\frac{12}{5}& = & -7x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1650}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1650x \color{red}{-132} & = & \color{red}{-385x} +40 \\\Leftrightarrow & -1650x \color{red}{-132} \color{blue}{+132} \color{blue}{+385x} & = & \color{red}{-385x} +40 \color{blue}{+385x} \color{blue}{+132} \\\Leftrightarrow & -1650x+385x& = & 40+132 \\\Leftrightarrow & \color{red}{-1265} x& = & 172 \\\Leftrightarrow & x = \frac{172}{-1265} & & \\\Leftrightarrow & x = \frac{-172}{1265} & & \\ & V = \left\{ \frac{-172}{1265} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{3}{10})& = & -4x+\frac{9}{10} \\\Leftrightarrow & -15x+\frac{9}{10}& = & -4x+\frac{9}{10} \\ & & & \text{kgv van noemers 10 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-150}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} })& = & (\frac{-40}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -150x \color{red}{+9} & = & \color{red}{-40x} +9 \\\Leftrightarrow & -150x \color{red}{+9} \color{blue}{-9} \color{blue}{+40x} & = & \color{red}{-40x} +9 \color{blue}{+40x} \color{blue}{-9} \\\Leftrightarrow & -150x+40x& = & 9-9 \\\Leftrightarrow & \color{red}{-110} x& = & 0 \\\Leftrightarrow & x = \frac{0}{-110} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{3}{11})& = & -5x+\frac{10}{3} \\\Leftrightarrow & 12x-\frac{12}{11}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{396}{ \color{blue}{33} }x- \frac{36}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 396x \color{red}{-36} & = & \color{red}{-165x} +110 \\\Leftrightarrow & 396x \color{red}{-36} \color{blue}{+36} \color{blue}{+165x} & = & \color{red}{-165x} +110 \color{blue}{+165x} \color{blue}{+36} \\\Leftrightarrow & 396x+165x& = & 110+36 \\\Leftrightarrow & \color{red}{561} x& = & 146 \\\Leftrightarrow & x = \frac{146}{561} & & \\ & V = \left\{ \frac{146}{561} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{4}{3})& = & -5x+\frac{10}{3} \\\Leftrightarrow & 8x-\frac{16}{3}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{24}{ \color{blue}{3} }x- \frac{16}{ \color{blue}{3} })& = & (\frac{-15}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 24x \color{red}{-16} & = & \color{red}{-15x} +10 \\\Leftrightarrow & 24x \color{red}{-16} \color{blue}{+16} \color{blue}{+15x} & = & \color{red}{-15x} +10 \color{blue}{+15x} \color{blue}{+16} \\\Leftrightarrow & 24x+15x& = & 10+16 \\\Leftrightarrow & \color{red}{39} x& = & 26 \\\Leftrightarrow & x = \frac{26}{39} & & \\\Leftrightarrow & x = \frac{2}{3} & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{5}{3})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 10x+\frac{10}{3}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{150}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 150x \color{red}{+50} & = & \color{red}{105x} +18 \\\Leftrightarrow & 150x \color{red}{+50} \color{blue}{-50} \color{blue}{-105x} & = & \color{red}{105x} +18 \color{blue}{-105x} \color{blue}{-50} \\\Leftrightarrow & 150x-105x& = & 18-50 \\\Leftrightarrow & \color{red}{45} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{45} & & \\ & V = \left\{ \frac{-32}{45} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{2}{3})& = & 4x+\frac{9}{4} \\\Leftrightarrow & 21x-\frac{14}{3}& = & 4x+\frac{9}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{252}{ \color{blue}{12} }x- \frac{56}{ \color{blue}{12} })& = & (\frac{48}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 252x \color{red}{-56} & = & \color{red}{48x} +27 \\\Leftrightarrow & 252x \color{red}{-56} \color{blue}{+56} \color{blue}{-48x} & = & \color{red}{48x} +27 \color{blue}{-48x} \color{blue}{+56} \\\Leftrightarrow & 252x-48x& = & 27+56 \\\Leftrightarrow & \color{red}{204} x& = & 83 \\\Leftrightarrow & x = \frac{83}{204} & & \\ & V = \left\{ \frac{83}{204} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{3}{5})& = & -9x+\frac{8}{3} \\\Leftrightarrow & -8x+\frac{12}{5}& = & -9x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-120}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -120x \color{red}{+36} & = & \color{red}{-135x} +40 \\\Leftrightarrow & -120x \color{red}{+36} \color{blue}{-36} \color{blue}{+135x} & = & \color{red}{-135x} +40 \color{blue}{+135x} \color{blue}{-36} \\\Leftrightarrow & -120x+135x& = & 40-36 \\\Leftrightarrow & \color{red}{15} x& = & 4 \\\Leftrightarrow & x = \frac{4}{15} & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{2}{11})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -20x+\frac{10}{11}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1100}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1100x \color{red}{+50} & = & \color{red}{385x} +66 \\\Leftrightarrow & -1100x \color{red}{+50} \color{blue}{-50} \color{blue}{-385x} & = & \color{red}{385x} +66 \color{blue}{-385x} \color{blue}{-50} \\\Leftrightarrow & -1100x-385x& = & 66-50 \\\Leftrightarrow & \color{red}{-1485} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-1485} & & \\\Leftrightarrow & x = \frac{-16}{1485} & & \\ & V = \left\{ \frac{-16}{1485} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{2}{7})& = & 8x+\frac{6}{5} \\\Leftrightarrow & -15x+\frac{10}{7}& = & 8x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-525}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} })& = & (\frac{280}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -525x \color{red}{+50} & = & \color{red}{280x} +42 \\\Leftrightarrow & -525x \color{red}{+50} \color{blue}{-50} \color{blue}{-280x} & = & \color{red}{280x} +42 \color{blue}{-280x} \color{blue}{-50} \\\Leftrightarrow & -525x-280x& = & 42-50 \\\Leftrightarrow & \color{red}{-805} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-805} & & \\\Leftrightarrow & x = \frac{8}{805} & & \\ & V = \left\{ \frac{8}{805} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{5}{11})& = & 8x+\frac{9}{2} \\\Leftrightarrow & -18x+\frac{30}{11}& = & 8x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-396}{ \color{blue}{22} }x+ \frac{60}{ \color{blue}{22} })& = & (\frac{176}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -396x \color{red}{+60} & = & \color{red}{176x} +99 \\\Leftrightarrow & -396x \color{red}{+60} \color{blue}{-60} \color{blue}{-176x} & = & \color{red}{176x} +99 \color{blue}{-176x} \color{blue}{-60} \\\Leftrightarrow & -396x-176x& = & 99-60 \\\Leftrightarrow & \color{red}{-572} x& = & 39 \\\Leftrightarrow & x = \frac{39}{-572} & & \\\Leftrightarrow & x = \frac{-3}{44} & & \\ & V = \left\{ \frac{-3}{44} \right\} & \\\end{align}\)