Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{4}{11})& = & 7x+\frac{5}{4} \\\Leftrightarrow & 8x-\frac{16}{11}& = & 7x+\frac{5}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{352}{ \color{blue}{44} }x- \frac{64}{ \color{blue}{44} })& = & (\frac{308}{ \color{blue}{44} }x+ \frac{55}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 352x \color{red}{-64} & = & \color{red}{308x} +55 \\\Leftrightarrow & 352x \color{red}{-64} \color{blue}{+64} \color{blue}{-308x} & = & \color{red}{308x} +55 \color{blue}{-308x} \color{blue}{+64} \\\Leftrightarrow & 352x-308x& = & 55+64 \\\Leftrightarrow & \color{red}{44} x& = & 119 \\\Leftrightarrow & x = \frac{119}{44} & & \\ & V = \left\{ \frac{119}{44} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{4}{5})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -6x+\frac{12}{5}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-90}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -90x \color{red}{+36} & = & \color{red}{105x} +50 \\\Leftrightarrow & -90x \color{red}{+36} \color{blue}{-36} \color{blue}{-105x} & = & \color{red}{105x} +50 \color{blue}{-105x} \color{blue}{-36} \\\Leftrightarrow & -90x-105x& = & 50-36 \\\Leftrightarrow & \color{red}{-195} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-195} & & \\\Leftrightarrow & x = \frac{-14}{195} & & \\ & V = \left\{ \frac{-14}{195} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{4}{11})& = & -7x+\frac{3}{2} \\\Leftrightarrow & -6x+\frac{12}{11}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-132}{ \color{blue}{22} }x+ \frac{24}{ \color{blue}{22} })& = & (\frac{-154}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -132x \color{red}{+24} & = & \color{red}{-154x} +33 \\\Leftrightarrow & -132x \color{red}{+24} \color{blue}{-24} \color{blue}{+154x} & = & \color{red}{-154x} +33 \color{blue}{+154x} \color{blue}{-24} \\\Leftrightarrow & -132x+154x& = & 33-24 \\\Leftrightarrow & \color{red}{22} x& = & 9 \\\Leftrightarrow & x = \frac{9}{22} & & \\ & V = \left\{ \frac{9}{22} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{2}{11})& = & 5x+\frac{2}{5} \\\Leftrightarrow & -9x+\frac{6}{11}& = & 5x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-495}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -495x \color{red}{+30} & = & \color{red}{275x} +22 \\\Leftrightarrow & -495x \color{red}{+30} \color{blue}{-30} \color{blue}{-275x} & = & \color{red}{275x} +22 \color{blue}{-275x} \color{blue}{-30} \\\Leftrightarrow & -495x-275x& = & 22-30 \\\Leftrightarrow & \color{red}{-770} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-770} & & \\\Leftrightarrow & x = \frac{4}{385} & & \\ & V = \left\{ \frac{4}{385} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{2}{7})& = & 7x+\frac{2}{5} \\\Leftrightarrow & 10x+\frac{10}{7}& = & 7x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{350}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 350x \color{red}{+50} & = & \color{red}{245x} +14 \\\Leftrightarrow & 350x \color{red}{+50} \color{blue}{-50} \color{blue}{-245x} & = & \color{red}{245x} +14 \color{blue}{-245x} \color{blue}{-50} \\\Leftrightarrow & 350x-245x& = & 14-50 \\\Leftrightarrow & \color{red}{105} x& = & -36 \\\Leftrightarrow & x = \frac{-36}{105} & & \\\Leftrightarrow & x = \frac{-12}{35} & & \\ & V = \left\{ \frac{-12}{35} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{4}{11})& = & -4x+\frac{2}{11} \\\Leftrightarrow & -18x-\frac{24}{11}& = & -4x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-198}{ \color{blue}{11} }x- \frac{24}{ \color{blue}{11} })& = & (\frac{-44}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -198x \color{red}{-24} & = & \color{red}{-44x} +2 \\\Leftrightarrow & -198x \color{red}{-24} \color{blue}{+24} \color{blue}{+44x} & = & \color{red}{-44x} +2 \color{blue}{+44x} \color{blue}{+24} \\\Leftrightarrow & -198x+44x& = & 2+24 \\\Leftrightarrow & \color{red}{-154} x& = & 26 \\\Leftrightarrow & x = \frac{26}{-154} & & \\\Leftrightarrow & x = \frac{-13}{77} & & \\ & V = \left\{ \frac{-13}{77} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{2}{3})& = & 3x+\frac{7}{2} \\\Leftrightarrow & -8x+\frac{8}{3}& = & 3x+\frac{7}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-48}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} })& = & (\frac{18}{ \color{blue}{6} }x+ \frac{21}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -48x \color{red}{+16} & = & \color{red}{18x} +21 \\\Leftrightarrow & -48x \color{red}{+16} \color{blue}{-16} \color{blue}{-18x} & = & \color{red}{18x} +21 \color{blue}{-18x} \color{blue}{-16} \\\Leftrightarrow & -48x-18x& = & 21-16 \\\Leftrightarrow & \color{red}{-66} x& = & 5 \\\Leftrightarrow & x = \frac{5}{-66} & & \\\Leftrightarrow & x = \frac{-5}{66} & & \\ & V = \left\{ \frac{-5}{66} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{2}{5})& = & 5x+\frac{5}{11} \\\Leftrightarrow & 12x-\frac{12}{5}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{-132} & = & \color{red}{275x} +25 \\\Leftrightarrow & 660x \color{red}{-132} \color{blue}{+132} \color{blue}{-275x} & = & \color{red}{275x} +25 \color{blue}{-275x} \color{blue}{+132} \\\Leftrightarrow & 660x-275x& = & 25+132 \\\Leftrightarrow & \color{red}{385} x& = & 157 \\\Leftrightarrow & x = \frac{157}{385} & & \\ & V = \left\{ \frac{157}{385} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{5}{7})& = & 5x+\frac{2}{9} \\\Leftrightarrow & 12x+\frac{30}{7}& = & 5x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{756}{ \color{blue}{63} }x+ \frac{270}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 756x \color{red}{+270} & = & \color{red}{315x} +14 \\\Leftrightarrow & 756x \color{red}{+270} \color{blue}{-270} \color{blue}{-315x} & = & \color{red}{315x} +14 \color{blue}{-315x} \color{blue}{-270} \\\Leftrightarrow & 756x-315x& = & 14-270 \\\Leftrightarrow & \color{red}{441} x& = & -256 \\\Leftrightarrow & x = \frac{-256}{441} & & \\ & V = \left\{ \frac{-256}{441} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{3}{7})& = & -9x+\frac{3}{11} \\\Leftrightarrow & 4x-\frac{6}{7}& = & -9x+\frac{3}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{308}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{21}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 308x \color{red}{-66} & = & \color{red}{-693x} +21 \\\Leftrightarrow & 308x \color{red}{-66} \color{blue}{+66} \color{blue}{+693x} & = & \color{red}{-693x} +21 \color{blue}{+693x} \color{blue}{+66} \\\Leftrightarrow & 308x+693x& = & 21+66 \\\Leftrightarrow & \color{red}{1001} x& = & 87 \\\Leftrightarrow & x = \frac{87}{1001} & & \\ & V = \left\{ \frac{87}{1001} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{4}{3})& = & -7x+\frac{2}{7} \\\Leftrightarrow & 16x+\frac{16}{3}& = & -7x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{336}{ \color{blue}{21} }x+ \frac{112}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 336x \color{red}{+112} & = & \color{red}{-147x} +6 \\\Leftrightarrow & 336x \color{red}{+112} \color{blue}{-112} \color{blue}{+147x} & = & \color{red}{-147x} +6 \color{blue}{+147x} \color{blue}{-112} \\\Leftrightarrow & 336x+147x& = & 6-112 \\\Leftrightarrow & \color{red}{483} x& = & -106 \\\Leftrightarrow & x = \frac{-106}{483} & & \\ & V = \left\{ \frac{-106}{483} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{4}{3})& = & 7x+\frac{8}{3} \\\Leftrightarrow & 15x-\frac{20}{3}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{45}{ \color{blue}{3} }x- \frac{20}{ \color{blue}{3} })& = & (\frac{21}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 45x \color{red}{-20} & = & \color{red}{21x} +8 \\\Leftrightarrow & 45x \color{red}{-20} \color{blue}{+20} \color{blue}{-21x} & = & \color{red}{21x} +8 \color{blue}{-21x} \color{blue}{+20} \\\Leftrightarrow & 45x-21x& = & 8+20 \\\Leftrightarrow & \color{red}{24} x& = & 28 \\\Leftrightarrow & x = \frac{28}{24} & & \\\Leftrightarrow & x = \frac{7}{6} & & \\ & V = \left\{ \frac{7}{6} \right\} & \\\end{align}\)