Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{3}{8})& = & 2x+\frac{3}{4} \\\Leftrightarrow & 21x-\frac{21}{8}& = & 2x+\frac{3}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{168}{ \color{blue}{8} }x- \frac{21}{ \color{blue}{8} })& = & (\frac{16}{ \color{blue}{8} }x+ \frac{6}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 168x \color{red}{-21} & = & \color{red}{16x} +6 \\\Leftrightarrow & 168x \color{red}{-21} \color{blue}{+21} \color{blue}{-16x} & = & \color{red}{16x} +6 \color{blue}{-16x} \color{blue}{+21} \\\Leftrightarrow & 168x-16x& = & 6+21 \\\Leftrightarrow & \color{red}{152} x& = & 27 \\\Leftrightarrow & x = \frac{27}{152} & & \\ & V = \left\{ \frac{27}{152} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{3}{11})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -10x+\frac{6}{11}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-110}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -110x \color{red}{+6} & = & \color{red}{-77x} +6 \\\Leftrightarrow & -110x \color{red}{+6} \color{blue}{-6} \color{blue}{+77x} & = & \color{red}{-77x} +6 \color{blue}{+77x} \color{blue}{-6} \\\Leftrightarrow & -110x+77x& = & 6-6 \\\Leftrightarrow & \color{red}{-33} x& = & 0 \\\Leftrightarrow & x = \frac{0}{-33} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{4}{7})& = & 9x+\frac{2}{9} \\\Leftrightarrow & -25x-\frac{20}{7}& = & 9x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1575}{ \color{blue}{63} }x- \frac{180}{ \color{blue}{63} })& = & (\frac{567}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1575x \color{red}{-180} & = & \color{red}{567x} +14 \\\Leftrightarrow & -1575x \color{red}{-180} \color{blue}{+180} \color{blue}{-567x} & = & \color{red}{567x} +14 \color{blue}{-567x} \color{blue}{+180} \\\Leftrightarrow & -1575x-567x& = & 14+180 \\\Leftrightarrow & \color{red}{-2142} x& = & 194 \\\Leftrightarrow & x = \frac{194}{-2142} & & \\\Leftrightarrow & x = \frac{-97}{1071} & & \\ & V = \left\{ \frac{-97}{1071} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{3}{11})& = & 9x+\frac{9}{2} \\\Leftrightarrow & -4x+\frac{6}{11}& = & 9x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-88}{ \color{blue}{22} }x+ \frac{12}{ \color{blue}{22} })& = & (\frac{198}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -88x \color{red}{+12} & = & \color{red}{198x} +99 \\\Leftrightarrow & -88x \color{red}{+12} \color{blue}{-12} \color{blue}{-198x} & = & \color{red}{198x} +99 \color{blue}{-198x} \color{blue}{-12} \\\Leftrightarrow & -88x-198x& = & 99-12 \\\Leftrightarrow & \color{red}{-286} x& = & 87 \\\Leftrightarrow & x = \frac{87}{-286} & & \\\Leftrightarrow & x = \frac{-87}{286} & & \\ & V = \left\{ \frac{-87}{286} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{4}{11})& = & 5x+\frac{10}{3} \\\Leftrightarrow & -24x+\frac{24}{11}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-792}{ \color{blue}{33} }x+ \frac{72}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -792x \color{red}{+72} & = & \color{red}{165x} +110 \\\Leftrightarrow & -792x \color{red}{+72} \color{blue}{-72} \color{blue}{-165x} & = & \color{red}{165x} +110 \color{blue}{-165x} \color{blue}{-72} \\\Leftrightarrow & -792x-165x& = & 110-72 \\\Leftrightarrow & \color{red}{-957} x& = & 38 \\\Leftrightarrow & x = \frac{38}{-957} & & \\\Leftrightarrow & x = \frac{-38}{957} & & \\ & V = \left\{ \frac{-38}{957} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{4}{9})& = & 5x+\frac{5}{11} \\\Leftrightarrow & 21x-\frac{28}{9}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2079}{ \color{blue}{99} }x- \frac{308}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{45}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2079x \color{red}{-308} & = & \color{red}{495x} +45 \\\Leftrightarrow & 2079x \color{red}{-308} \color{blue}{+308} \color{blue}{-495x} & = & \color{red}{495x} +45 \color{blue}{-495x} \color{blue}{+308} \\\Leftrightarrow & 2079x-495x& = & 45+308 \\\Leftrightarrow & \color{red}{1584} x& = & 353 \\\Leftrightarrow & x = \frac{353}{1584} & & \\ & V = \left\{ \frac{353}{1584} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{4}{7})& = & -7x+\frac{6}{11} \\\Leftrightarrow & 12x+\frac{16}{7}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x+ \frac{176}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{+176} & = & \color{red}{-539x} +42 \\\Leftrightarrow & 924x \color{red}{+176} \color{blue}{-176} \color{blue}{+539x} & = & \color{red}{-539x} +42 \color{blue}{+539x} \color{blue}{-176} \\\Leftrightarrow & 924x+539x& = & 42-176 \\\Leftrightarrow & \color{red}{1463} x& = & -134 \\\Leftrightarrow & x = \frac{-134}{1463} & & \\ & V = \left\{ \frac{-134}{1463} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{5}{11})& = & -7x+\frac{8}{3} \\\Leftrightarrow & -10x+\frac{25}{11}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-330}{ \color{blue}{33} }x+ \frac{75}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -330x \color{red}{+75} & = & \color{red}{-231x} +88 \\\Leftrightarrow & -330x \color{red}{+75} \color{blue}{-75} \color{blue}{+231x} & = & \color{red}{-231x} +88 \color{blue}{+231x} \color{blue}{-75} \\\Leftrightarrow & -330x+231x& = & 88-75 \\\Leftrightarrow & \color{red}{-99} x& = & 13 \\\Leftrightarrow & x = \frac{13}{-99} & & \\\Leftrightarrow & x = \frac{-13}{99} & & \\ & V = \left\{ \frac{-13}{99} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{5}{2})& = & 5x+\frac{5}{6} \\\Leftrightarrow & 6x-\frac{15}{2}& = & 5x+\frac{5}{6} \\ & & & \text{kgv van noemers 2 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{36}{ \color{blue}{6} }x- \frac{45}{ \color{blue}{6} })& = & (\frac{30}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 36x \color{red}{-45} & = & \color{red}{30x} +5 \\\Leftrightarrow & 36x \color{red}{-45} \color{blue}{+45} \color{blue}{-30x} & = & \color{red}{30x} +5 \color{blue}{-30x} \color{blue}{+45} \\\Leftrightarrow & 36x-30x& = & 5+45 \\\Leftrightarrow & \color{red}{6} x& = & 50 \\\Leftrightarrow & x = \frac{50}{6} & & \\\Leftrightarrow & x = \frac{25}{3} & & \\ & V = \left\{ \frac{25}{3} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{3}{5})& = & 7x+\frac{5}{2} \\\Leftrightarrow & 30x-\frac{18}{5}& = & 7x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{300}{ \color{blue}{10} }x- \frac{36}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 300x \color{red}{-36} & = & \color{red}{70x} +25 \\\Leftrightarrow & 300x \color{red}{-36} \color{blue}{+36} \color{blue}{-70x} & = & \color{red}{70x} +25 \color{blue}{-70x} \color{blue}{+36} \\\Leftrightarrow & 300x-70x& = & 25+36 \\\Leftrightarrow & \color{red}{230} x& = & 61 \\\Leftrightarrow & x = \frac{61}{230} & & \\ & V = \left\{ \frac{61}{230} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{5}{6})& = & 7x+\frac{8}{3} \\\Leftrightarrow & 20x-\frac{25}{6}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 6 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{120}{ \color{blue}{6} }x- \frac{25}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 120x \color{red}{-25} & = & \color{red}{42x} +16 \\\Leftrightarrow & 120x \color{red}{-25} \color{blue}{+25} \color{blue}{-42x} & = & \color{red}{42x} +16 \color{blue}{-42x} \color{blue}{+25} \\\Leftrightarrow & 120x-42x& = & 16+25 \\\Leftrightarrow & \color{red}{78} x& = & 41 \\\Leftrightarrow & x = \frac{41}{78} & & \\ & V = \left\{ \frac{41}{78} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{5}{4})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -6x+\frac{15}{4}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-120}{ \color{blue}{20} }x+ \frac{75}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -120x \color{red}{+75} & = & \color{red}{-140x} +24 \\\Leftrightarrow & -120x \color{red}{+75} \color{blue}{-75} \color{blue}{+140x} & = & \color{red}{-140x} +24 \color{blue}{+140x} \color{blue}{-75} \\\Leftrightarrow & -120x+140x& = & 24-75 \\\Leftrightarrow & \color{red}{20} x& = & -51 \\\Leftrightarrow & x = \frac{-51}{20} & & \\ & V = \left\{ \frac{-51}{20} \right\} & \\\end{align}\)